University of the People MATH 1280: Questions and Answers Latest Winter 2026.

University of the People MATH 1280: Questions and Answers Latest Winter 2026. Questions Weeks 1. Why is the Central Limit Theorem important in statistics? a. It guarantees the accuracy of all statistical tests. b. It eliminates all forms of bias in sampling. c. It provides a way to estimate population parameters. d. It shows that all data is normally distributed. 2. A study shows the mean age of tablet users is 34 years with a standard deviation of 15 years. For a sample size of 100, what is the probability that the sample mean age exceeds 30 years? a. 0.9812 b. 0.9735 c. 0 d. 0.9962 3. Richard’s Furniture Company delivers furniture from 10 A.M. to 2 P.M. continuously and uniformly. We are interested in how long (in hours) past the 10 A.M. start time that individuals wait for their delivery. The average wait time is: a. two hours. b. one hour. c. two and a half hours. d. four hours. 4. Which of the following best describes the standard deviation of the sampling distribution of the sample means? a. It is larger than the population standard deviation. b. It is smaller than the population standard deviation. c. It is the same as the population standard deviation. d. It is always equal to zero. 5. If a population has a mean of 50 and a standard deviation of 5, what is the mean of the sample mean for a sample size of 40? a. 10 b. 5 c. 50 d. 45 6. In a busy hospital, the average time between two consecutive patient arrivals at the emergency room is 2 minutes with a standard deviation of 0.5 minutes. For a random sample of 100 such arrival times, what is the probability that the average time between arrivals is between 1.75 minutes and 1.85 minutes? a. 0.0013 b. 0.013 c. 0.015 d. 0.00157. One year, the distribution of salaries for professional sports players had mean $1.6 million and standard deviation $0.7 million. Suppose a sample of 100 major league players was taken. The approximate probability that the average salary of the 100 players that year exceeded $1.1 million would be 1. a. True b. False 8. Which of these statements best describes the effect of sample size on the Central Limit Theorem? a. Sample size has no effect. b. Smaller sample sizes make the sample mean closer to the population mean. c. Larger sample sizes make the sampling distribution closer to normal. d. Smaller sample sizes produce normal sampling distributions. 9. Given the same unknown distribution with μx=60, n=100 and σx=10, what is the Zscore corresponding to ΣX=2500? a. -35 b. 5 c. 4 d. 2 10. For a population with mean (μ) of 30 and standard deviation (σ) of 5, the mean of the sum of the sample values (ΣX) for a sample size of 50 is __. a. 3000 b. 600 c. 1000 d. 1500 11. How does the Central Limit Theorem enable the use of sample means in hypothesis testing? a. It allows for the calculation of probability values using sample means. b. It ensures that all hypotheses are correct. c. It requires only qualitative data. d. It eliminates the need for sample sizes. 12. Systolic blood pressure for women between the ages of 18 to 24 follow a normal distribution with a standard deviation of 13.1. If one woman from this population is randomly selected, find the probability that her systolic blood pressure is greater than 120. a. 50% b. 40% c. 35% d. 45% 13. Which of the following conditions typically increases the applicability of the Central Limit Theorem? a. The population must be normally distributed.b. The sample size must be smaller than 10. c. The sample size must be at least 30. d. The population must be finite. 14. When the sample size increases, the variability of the sample mean is ______. a. decreases. b. increases. c. stays the same. d. becomes unpredictable. 15. If the population standard deviation is 10 and the sample size is 25, then the standard error of the mean will be 2. a. False b. True 16. The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours. A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours. a. 0 b. 10 c. 15 d. 1 17. As the sample size gets larger, the standard error of the sampling distribution of the sample mean gets larger as well. a. False b. True 18. The mean number of minutes for app engagement by a tablet user is 8.2 minutes. Suppose the standard deviation is one minute. Take a sample of 60. Find the 90th percentile for the sample mean time for app engagement for a tablet user. a. 8.5 minutes b. 8.37 minutes c. 8.2 minutes d. 8 minutes 19. What is the 90th percentile for the sum of the 25 values of x? (Use z≈1.281 for the 90th percentile, μx=30 and σx=5) a. 850 b. 782 c. 900 d. 750 20. The mean number of minutes for app engagement by a tablet user is 8.2 minutes. Suppose the standard deviation is one minute. Take a sample of 60. Find the probability that the sample mean is between eight minutes and 8.5 minutes.a. 0.9293 b. 0.9025 c. 0.9180 d. 0.9123 21. Consider a random sample of 144 customers who exceed the time allowance included in their basic cell phone contract. μ = 22 and σ = 22. Find P(Σx is at least 3,000). a. 0.7377 b. 0.7919 c. 0.4521 d. 0.4029 22. An unknown distribution has a mean of 90 and a standard deviation of 15. A sample of size 80 is drawn randomly from the population. Find the probability that the sum of the 80 values is more than 7,500. a. 0.00125% b. 1.25% c. 12.5% d. 0.125% 23. The Central Limit Theorem is primarily used to: a. Justify the normal approximation for large samples. b. Change the population mean. c. Reduce data variability. d. Compute the median of a population. 24. Given a population with a mean age of 34 years and standard deviation of 15 years, for a sample of size 100, find the 95th percentile of the sample mean age. a. 36.5 b. 36 c. 34.5 d. 34 25. If the sum of sample values has a Z-score of 2, it indicates that the sum is ____ standard deviations above the mean. a. 1 b. 2 c. 3 d. 4 26. Consider a random sample of 144 customers who exceed the time allowance included in their basic cell phone contract. μ = 22 and σ = 22. Find the 75th percentile for the sample mean excess time of these customers. a. 22.5 b. 22 c. 23d. 23.2 27. The Central Limit Theorem is important because: a. It allows us to make inferences about population parameters using sample data. b. It increases the standard deviation. c. It reduces the variability in the population. d. It tells us that any distribution is normal. 28. For a population with μx=50 and σx=12, if a sample of 100 is drawn, what is the probability that the sum of the sample values exceeds 5200? a. 0.200 b. 0.050 c. 0.0475 d. 0.100 29. If the Z-score for a sum of sample values is 2 for the distribution with mean of ΣX = 30 and standard deviation of ΣX = 5, the corresponding ΣX is ______. a. 90 b. 40 c. 80 d. 100 30. For a different distribution with μx=30 and σx=5, if a sample of size 25 is drawn, what is the mean of the sum of the sample values (ΣX)? a. 1500 b. 7500 c. 750 d. 600 31. A large union wants to estimate the mean monthly hours members are absent. They randomly sampled 468 members and recorded their absences for one month. Which of the following should be used to estimate the parameter of interest for this problem? a. A large sample confidence interval for mean. b. A large sample confidence interval for proportion. c. A small sample confidence interval for proportion. d. A small sample confidence interval for mean. 32. For a continuous random variable, what is the probability that it takes an exact value (e.g., X = a)? a. 0 b. Undefined c. 1 d. 0.533. Suppose the number of miles driven by a truck driver follows a uniform distribution between 300 and 700. How many miles does the driver travel on the furthest 10% of days? a. 590 b. 570 c. 750 d. 660 34. A continuous probability distribution is defined between x = 5 and x = 12. What is P(x = 15)? a. 0 b. 0.5 c. 1 d. 0.8 35. A distribution is given as X ∼ Exp(λ). Which is the relation between the mean and the median? a. The mean is smaller than the median. b. The mean is larger than the median. c. The mean and median cannot be determined. d. The mean and median are equal. 36. The number of miles driven by a truck driver falls between 300 and 700 and follows a uniform distribution. At least how many miles does the truck driver travel on the furthest 10% of days? a. 660 b. 570 c. 590 d. 750 37. For a continuous uniform distribution between 0 and 5, the probability that the random variable takes a value less than 3 is: a. 1 b. 0.5 c. 0.6 d. 0.4 38. In exponential distribution, the term "memoryless" means that the probability of an event occurring in the future is __________. a. higher with more time b. affected by the number of events c. independent of the past d. dependent on past events 39. The area under the curve of the probability density function of a continuous random variable represents: a. Probabilityb. Standard deviation c. Mean d. Variance 40. For a Poisson distribution with rate λ = 5, what is the expected value of the random variable X? a. 1/5 b. 1 c. 10 d. 5 41. If the exponential distribution has a rate of 2 events per hour, what is the probability that no events occur in the first 30 minutes? a. e^(-0.6) b. 1 - e^(-1) c. e^(-1) d. 1 - e^(-0.6) 42. The total probability of a continuous random variable must always be greater than 1. a. False b. True 43. A continuous probability distribution has a probability density function (PDF) where the total area under the curve is ______. a. 1 b. 0 c. ∞ d. 10 44. A machine part has a lifetime that is uniformly distributed between 0 and 1000 hours. What is the probability that a randomly selected machine part lasts between 400 and 600 hours? a. 0.04 b. 0.02 c. 0.2 d. 0.4 45. The uniform distribution is most commonly used to model: a. Random events with equal probability b. Normal-like data c. Skewed data d. Data with discrete outcomes 46. For a continuous random variable X, the probability that X = a (where a is a constant) is always: a. a b. Undefinedc. 0 d. 1 47. A factory produces widgets, and the weight of each widget is uniformly distributed between 50 and 70 grams. What is the probability that a randomly selected widget weighs more than 60 grams? a. 0.3 b. 0.5 c. 0.25 d. 0.75 48. The exponential distribution is often used to model which of the following? a. The number of customers arriving at a store b. The height of plants c. The number of heads in 10-coin tosses d. The time between the arrivals of customers at a store 49. Ace Heating and Air Conditioning Service finds that the time needed to fix a furnace is uniformly distributed between 1.5 and 4 hours. Find the minimum time for the longest 25% of repair times and the corresponding percentile. a. 3.5 hours, 90th percentile b. 3 hours, 50th percentile c. 3.375 hours, 75th percentile d. 2.75 hours, 25th percentile 50. Which of the following is an example of a continuous random variable? a. The number of heads in a coin toss b. The number of students in a classroom c. The height of a person d. The number of cars in a parking lot 51. The length of a phone call, in minutes, is an exponential random variable with a decay parameter λ = 1/12. If another person arrives at a public telephone just before you, what is the probability that you will have to wait more than 5 minutes? a. 0.50 b. 0.66 c. 0.75 d. 0.33 52. Which of the following statements about the Poisson and Exponential distributions is true? a. Both distributions are discrete. b. Both distributions are continuous. c. The Poisson distribution is discrete, while the Exponential distribution is continuous. d. The Exponential distribution is discrete, while the Poisson distribution is continuous.53. For an exponential distribution with rate parameter λ = 2, find the value of k such that P(X k) = 0.75. a. 0.693 b. -0.693 c. -0.280 d. 0.280 54. In a continuous distribution with a mean of 10 and a standard deviation of 2, what is the variance? a. 10 b. 12 c. 4 d. 2 55. In a small city, the number of automobile accidents occurs with a Poisson distribution at an average of three per week. What is the probability that there are at most 2 accidents in any given week? a. 0.302 b. 0.149 c. 0.423 d. 0.224 56. The time between customer arrivals at a service center follows an exponential distribution with a rate parameter of 0.1 customers per minute. What is the 80th percentile of the time between customer arrivals? a. 15.30 minutes b. 20.46 minutes c. 12.33 minutes d. 16.09 minutes 57. For a continuous random variable, why is the probability of X being exactly equal to a specific value (P(X = a)) zero? a. Because the total probability is greater than 1. b. Because the variable cannot take specific values. c. Because continuous random variables have no defined outcomes. d. Because there are infinitely many possible values for X. 58. For a continuous probability distribution defined for 0 ≤ x ≤ 13, what is the value of P(x 13)? a. 0 b. Infinite c. 1 d. 0.99 59. If the rate of events occurring is 4 per hour, then the variance of the time between events in an exponential distribution is __________.a. 0.05 hours b. 4 hours c. 0.0625 hours d. 1 hour 60. A car rental service has cars that are rented for a time between 1 and 10 hours. Find the probability that a car is rented for more than 7 hours, given that it was rented for more than 4 hours. a. 0.6 b. 0.7 c. 0.4 d. 0.5 61. The amount of time (in minutes) until the next train arrives at a train station is uniformly distributed between 10 and 30 minutes. Define the random variable X. a. X = the time (in minutes) until the next train arrives, where 10 ≤ X ≤ 30 b. X = the time (in seconds) until the next train arrives, where 10 ≤ X ≤ 30 c. X = the distance (in miles) between two train stations, where 10 ≤ X ≤ 30 d. X = the number of trains arriving at a station, where 10 ≤ X ≤ 30 62. The cumulative distribution function (CDF) of a continuous random variable is the ______ of the probability density function. a. Derivative b. Integral c. Logarithm d. Square 63. The variance of a uniform distribution between 2 and 10 is calculated as: a. 6.40 b. 2.31 c. 6.67 d. 5.33 64. The CDF of a continuous uniform distribution is a ______. a. Exponential function b. Bell-shaped curve c. Constant d. Linear function 65. Answer the question based on this Venn diagramWhat set of number represent event B? a. {2} b. {1,3,5} c. {2,3,5} 66. A University sample report a mean grade point average of 3.0. This value is an example of a: a. parameter b. data c. statistic d. variable 67. Which type of quantitative variable is the height of a NBA player classified as? a. continuous b. discrete X 1.7462 2.4291 2.3978 1.8295 2.0956 1.9801 2.0638 1.9862 1.8192 1.8221 1.9418 2.0916 68. Based on the above table, Find the third Quartile: a. 2.03 b. 2.09 c. 1.82X 1.7462 2.4291 2.3978 1.8295 2.0956 1.9801 2.0638 1.9862 1.8192 1.8221 1.9418 2.0916 69. Based on the above table, Find the Inter-Quartile range: a. 0.26 b. 0.41 c. 0.33 X 1.7462 2.4291 2.3978 1.8295 2.0956 1.9801 2.0638 1.9862 1.8192 1.8221 1.9418 2.0916 70. Based on the above table, Find the range: a. 0.70 b. 0.51 c. 0.68 71. In a survey of individuals who have been in a car crash in the past 20 years in the city of Douala in Cameroon, 40% of respondents reported yes. What represent this percentage? a. Statistic b. Parameter 72. Answer the question based on this Venn diagramWhat set of number represent event A AND B? a. {2} b. {3,5} c. {2,3,5} 73. 61% of the residents of Lagos, Nigeria are female. What represent this percentage? a. parameter b. statistic 74. Answer the question based on the dataset. 32, 32, 33, 34, 38, 40, 42, 42, 43, 44, 46, 47, 47, 48, 48, 48, 49, 50, 50, 51, 52, 52, 52, 53, 54, 56, 57, 57, 60, 61. What are the leaves of the stem 5? a. 0,0,1,2,2,2,3,4,6,7 b. 0,1,2,2,2,3,4,6,7,7 c. 0,0,1,2,2,2,3,4,6,7,7 X 1.7462 2.4291 2.3978 1.8295 2.0956 1.9801 2.0638 1.9862 1.8192 1.8221 1.9418 2.0916 75. Based on the above table, Find the Inter-Quartile range: a. 0.26b. 0.41 c. 0.33 X 1.7462 2.4291 2.3978 1.8295 2.0956 1.9801 2.0638 1.9862 1.8192 1.8221 1.9418 2.0916 76. Based on the above table, Find the median: a. 2.4301 b. 1.98315 c. 1.7467 77. In a study of college students in a state, a sample of 1000 students were taken from 20 colleges. The average grade of all college students in that state is a: a. a statistic. b. a parameter. c. the median. d. a population. e. none of the above 78. A University student population is represented in three age groups are followed: Student AgeGroup Student Proportion (%) 18–25 45% 26–44 36% 45–64 19% Which student age group represents the highest proportion? a. 18–25 b. 26–44 c. 45–64 X 1.7462 2.4291 2.3978 1.8295 2.09561.9801 2.0638 1.9862 1.8192 1.8221 1.9418 2.0916 79. Based on the above table, Find the max: a. 2.421 b. 2.291 c. 2.4291 X 1.7462 2.4291 2.3978 1.8295 2.0956 1.9801 2.0638 1.9862 1.8192 1.8221 1.9418 2.0916 80. Based on the above table, Find the average: a. 2.016917 b. 1 c. 3 81. Answer the question based on the dataset. 32, 32, 33, 34, 38, 40, 42, 42, 43, 44, 46, 47, 47, 48, 48, 48, 49, 50, 50, 51, 52, 52, 52, 53, 54, 56, 57, 57, 60, 61. Which stem has the highest number of leaves? a. 4 b. 3 c. 6 82. Answer the question based on the dataset. 32, 32, 33, 34, 38, 40, 42, 42, 43, 44, 46, 47, 47, 48, 48, 48, 49, 50, 50, 51, 52, 52, 52, 53, 54, 56, 57, 57, 60, 61. What is the list of stems of the data? a. 0,1,2,3,4,5,6 b. 3,4,5,6 c. 1,2,3,4,5,6X 1.7462 2.4291 2.3978 1.8295 2.0956 1.9801 2.0638 1.9862 1.8192 1.8221 1.9418 2.0916 83. Based on the above table, Find the min: a. 1.7462 b. 1.7400 c. 1.6000 X 1.7462 2.4291 2.3978 1.8295 2.0956 1.9801 2.0638 1.9862 1.8192 1.8221 1.9418 2.0916 84. Based on the above table, Find the variance: a. 0.012 b. 0.047 c. 0.033 85. A survey of 100 students found the number of books read per month as follows: 0 books (30 students), 1 book (40 students), 2 books (20 students), 3 books (10 students). The relative cumulative frequency for students who read up to 2 books is: a. 0.7 b. 1.0 c. 0.9 d. 0.886. A teacher recorded test scores as follows: 60, 70, 80, 90. The cumulative relative frequency for scores up to 80 is 0.75. How many students scored 90? a. 3 b. 2 c. Cannot be determined d. 1 87. A hotel recorded the number of room bookings made each day during the first week of March. The data were as follows: 12, 15, 10, 18, 20, 15, 22. Based on a bar plot of this data, the height of the bar for the value 15 would represent: a. 2 days where 15 bookings were made. b. 15 bookings across 2 days. c. The maximum number of bookings in the week. d. 1 day where 15 bookings were made. 88. Which term describes the entire group that a researcher is interested in studying? a. Parameter b. Variable c. Sample d. Population 89. The temperature of various cities on a given day is recorded in degrees Fahrenheit. The level of measurement is: a. Interval b. Ratio c. Nominal d. Ordinal 90. Which of the following is an example of ordinal data? a. Gender (e.g., male, female) b. Test scores (e.g., 90%, 85%) c. Number of cars sold d. Movie ratings (e.g., 1 star to 5 stars) 91. A frequency table for test scores shows that 70 students scored less than or equal to 80. The value 70 represents the: a. Relative frequency b. Absolute frequency c. Cumulative frequency d. Grouped frequency 92. A teacher is studying the performance of students in her school. She randomly selects one class from each grade and analyzes the test scores of all students in those classes. Which sampling technique does this represent? a. Stratified Sampling b. Simple Random Sampling c. Systematic Samplingd. Cluster Sampling 93. The __________ is the likelihood that a specific event will occur. a. hypothesis b. outcome c. probability d. parameter 94. A retail company is studying online shopping habits. It selects every 10th transaction from its database for analysis. What type of sampling method is being used? a. Simple Random Sampling b. Stratified Sampling c. Cluster Sampling d. Systematic Sampling 95. A group of participants were surveyed about their commute times: 5-10 minutes (10 participants), 11-15 minutes (20 participants), 16-20 minutes (10 participants). The relative frequency for participants with commute times of 11-15 minutes is: a. 0.4 b. 0.6 c. 0.5 d. 0.8 96. A researcher uses a frequency table to count how often different shoe sizes are purchased in a store. Shoe size is a: a. Continuous variable b. Discrete variable c. Ratio variable d. Nominal variable 97. Probability is the study of uncertainty and the likelihood of events occurring. a. True b. False 98. A call center recorded the number of customer calls handled per hour over 5 consecutive hours: 8, 10, 10, 12, 8. In a bar plot of this data, the bar for 8 calls would represent: a. The mode of the dataset. b. 2 hours with 8 calls. c. 8 hours with 2 calls. d. The total number of calls received in 2 hours. 99. A restaurant owner selects customers at random from their loyalty program database for a satisfaction survey. The selected customers are the: a. Sample b. Populationc. Census d. Parameter 100. A city’s transportation department conducted a survey to assess the satisfaction of bus riders. Researchers interviewed passengers at 15 randomly selected bus stops throughout the city during peak hours and asked, "Are you satisfied with the cleanliness of the buses?" The population in this survey is: a. Passengers at the 15 selected bus stops. b. The transportation department staff. c. All bus riders in the city. d. Researchers conducting the survey. 101. A factory manager reviews data summarizing the daily production of items over the last month. What type of statistics is being used? a. Descriptive Statistics b. Probability c. Predictive Analysis d. Inferential Statistics 102. A game developer wants to know how players feel about a new feature. They survey 200 randomly selected players worldwide. What type of data collection is this? a. Observation b. Survey c. Simulation d. Experiment 103. A factory recorded the number of defective products per batch: 5 (5 batches), 10 (3 batches), 15 (2 batches). The relative frequency of batches with 10 defective products is: a. 0.7 b. 0.3 c. 0.4 d. 0.5 104. A gym tracks the number of members attending different classes (Yoga, Zumba, Strength Training). What level of measurement is used? a. Ordinal b. Ratio c. Interval d. Nominal 105. In evaluating customer satisfaction, what is the primary purpose of statistics? a. To collect data only b. To create biased outcomes c. To manipulate numerical values d. To analyze and interpret data106. A bookstore recorded the number of customers on different days: 10, 15, 20, 25. The cumulative frequency of customers after three days is: a. 50 b. 15 c. 25 d. 45 107. The sample space is the set of all possible outcomes in a probability experiment. a. True b. False 108. A pharmaceutical company is testing a new drug and selects patients from various hospitals to participate in the trial. The company uses a list of hospital patients and picks every 5th patient on the list. What sampling technique is being applied? a. Cluster Sampling b. Convenience Sampling c. Systematic Sampling d. Stratified Sampling 109. The number of items sold daily at a grocery store during the first week of October is: 50, 60, 45, 70, 60, 80, 50. If a bar plot is drawn for this data, the height of the bar corresponding to 60 items represents: a. The median number of items sold in the week. b. The most frequent number of items sold. c. 2 days with 60 items sold. d. The total items sold across all days. 110. A farm records the number of apples picked each day over 7 days: 50, 60, 50, 70, 50, 60, 80. If a bar plot is created for this data, the bar for 60 apples represents: a. 60 apples picked across 2 days. b. The least frequent value in the data. c. 2 days with 60 apples picked. d. The median value of the dataset. 111. When measuring the height of individuals in a population for a health study, what type of variable allows for an infinite number of values within a given range? a. Discrete b. Ordinal c. Nominal d. Continuous 112. The daily profits of a coffee shop over a week are: $100, $150, $100, $200, $100, $150, $250. In the bar plot, the height of the bar for $100 represents: a. 3 days with $100 in profits. b. The least profitable day of the week.c. The average weekly profit. d. The most profitable day of the week. 113. A class of students was asked how many books they read in a month: 0, 1, 2, 3, 2, 1, 0, 2. In a frequency table, the frequency for the value 2 is: a. 5 b. 3 c. 4 d. 2 114. A research study categorizes participants based on their gender (male, female, non-binary). What level of measurement does this represent? a. Nominal b. Ordinal c. Ratio d. Interval 115. A school principal wants to understand students' preferences for extracurricular activities. She randomly selects students from each grade level to participate in a survey. This is an example of: a. Stratified Sampling b. Cluster Sampling c. Convenience Sampling d. Systematic Sampling 116. A city council wants to survey residents about a new park development. To ensure diverse input, they divide the city into neighborhoods and randomly select individuals from each neighborhood. What sampling method are they using? a. Cluster Sampling b. Simple Random Sampling c. Stratified Sampling d. Systematic Sampling 117. What is the shape of a histogram called if the bars gradually rise to a peak and then fall symmetrically? a. Bimodal distribution b. Uniform distribution c. Normal distribution d. Skewed distribution 118. For the data set: 2, 4, 6, 8, 10, what is the upper quartile (Q3)? a. 6 b. 7 c. 9 d. 8 119. What is the sum of expenditure on rent and others?a. 2,00,000 b. 4,00,000 c. 3,00,000 d. 1,00,000 120. The variance of a data set is 9. What is the standard deviation? a. 5 b. 3 c. 6 d. 9 121. In a box plot, if a data point lies beyond the upper whisker or lower whisker, it is typically considered an ______. a. Median. b. Mode. c. Outlier. d. Quartile. 122. To determine the median of a dataset, the data must be arranged in descending order. a. False b. True 123. Given a data set of 15 ordered values, the third quartile (Q3) would be the median of which group? a. The last 7 values. b. The last 8 values. c. The first 7 values. d. The first 8 values. 124. What is the typical criterion for identifying outliers using a box plot? a. Any data point outside the IQR + 1.5*IQR b. Any data point below the lower quartile or above the upper quartilec. Any data point beyond the maximum or minimum value d. Any data point more than 2 standard deviations from the mean 125. If a bar graph shows the number of pets owned by students in a class, a category on the x-axis could be ________. a. Total number of pets b. Number of students c. Types of pets (e.g., dogs, cats, birds) d. Average pet ownership per student 126. What does the stem represent in a stem-and-leaf plot? a. The individual data points b. The trailing digits of each data point c. The frequency of data d. The leading digits of each data point 127. The graph used to represent data that changes continuously over time is called a Line Graph. a. False b. True 128. If a new value is added to a data set that is significantly higher than the current mean, then the mean will decrease. a. True b. False 129. Given the following ordered dataset: 3, 7, 9, 12, 15, 18, 20, 25, 30, 35, what is the 50th percentile? a. 17.5 b. 16.5 c. 18.5 d. 12.5 130. The standard deviation of a data set with all equal values is _____. a. 1 b. The mean c. 0 d. Undefined 131. Based on the given histogram, what is the cumulative frequency for the class 500-600?a. 800 b. 650 c. 200 d. 500 132. A Time series graph is the most suitable for visualizing data such as monthly sales over a year. a. False b. True 133. Given the data set: 1, 2, 2, 3, 4, 4, 5, what is the mode? a. 4 b. 2 and 4 c. No mode d. 2 134. What is the mode of the following data set: 8, 10, 10, 15, 15, 15, 20? a. 8 b. 15 c. No mode d. 10 135. Which of the following data values would be classified as an outlier if the IQR is 10 and Q1 = 20, Q3 = 50? a. 70 b. 10 c. 30 d. 40 136. Given the following ordered dataset: 10, 15, 20, 25, 35, 40, 45, 50, find the 90th percentile.a. 38 b. 50 c. 40 d. 45 137. What is the median for this data set: 2, 4, 7, 9, 12? a. 5.5 b. 6 c. 4 d. 7 138. Which of the following is true about the range of a data set? a. It is the average of all values in the data set b. It is the difference between the largest and smallest values in the data set c. It is the middle value in the data set d. It is the sum of all the values in the data set 139. For the data set: 5, 7, 10, 12, 15, calculate the IQR. a. 3.5 b. 8.5 c. 7.5 d. 5.5 140. What type of data is best represented using a bar graph? a. Continuous data b. Time-series data c. Categorical data d. Interval data 141. In a time series graph, what typically represents the X-axis? a. Statistical measures b. Time periods c. Frequency d. Data values 142. For the data set: 5, 10, 15, 20, calculate the standard deviation. a. 3.59 b. 2.59 c. 4.59 d. 5.59 143. Observe the temperature-time graph and answer the following questions. What is the rise in temperature from 9 hours to 11 hours?a. 1 °F b. 2 °F c. 4 °F d. 3 °F 144. For the data set: 5, 10, 15, 20, 25, what is the mode? a. 10 b. 5 c. 15 d. No mode 145. How does an outlier affect the standard deviation of a dataset? a. It makes the standard deviation equal to 0 b. It has no effect on the standard deviation c. It decreases the standard deviation d. It increases the standard deviation 146. For the data set: 3, 5, 8, 10, 12, what is the lower quartile (Q1)? a. 8 b. 4 c. 5 d. 3 147. Which measure of central tendency is most affected by outliers? a. Mode b. Median c. Range d. Mean 148. Which of the following statements about histograms and bar graphs is true? a. Histograms and bar graphs are used interchangeably without any difference.b. Histograms represent categorical data, while bar graphs represent numerical data. c. Bar graphs use continuous intervals along the x-axis, while histograms use discrete intervals. d. Both histograms and bar graphs use bars to represent data, but histograms are for numerical data while bar graphs are for categorical data. 149. Given the data set: 3, 5, 7, 9, 11. What is the mean? a. 8 b. 5 c. 7 d. 6 150. What is the probability of getting a number greater than 6 on 1 dice? a. 0 b. 1/3 c. 1/2 d. 1 151. The contingency table below shows survey results of students’ preferred subjects: Likes Math Likes Science Total Male 20 15 35 Female 25 20 45 Total 45 35 80 What is the probability that a randomly selected student is a female who likes Math? a. 45/80 b. 25/80 c. 25/35 d. 20/80 152. A tree diagram is primarily used to: a. Analyze the relationship between two variables b. Show all possible outcomes of an event or process c. Represent the distribution of numerical data d. Visualize the intersection of two sets 153. Which of the following cannot be the value of probability? a. 1 b. 0 c. 0.5 d. -1 154. Which of the following diagrams best depicts the relationship among book, dictionary, and printer?a. b. c. d. 155. Two events are said to be mutually exclusive if ___________. a. the probability of their union is zero b. they can happen together c. the probability of their intersection is zero d. they are independent 156. What is the probability of a sure event? a. 1 b. 1/4 c. 1/2 d. 0 157. If A and B are mutually exclusive events, what is A∩B? a. Bc b. Ac c. A∪B d. ∅ (empty set) 158. Two events are independent if _____________. a. they occur simultaneously b. the probability of their union is zero c. the probability of one does not affect the probability of the other d. they cannot occur together159. The contingency table below shows survey results of students’ preferred subjects: Likes Math Likes Science Total Male 20 15 35 Female 25 20 45 Total 45 35 80 What is the probability that a randomly selected student likes Science, given they are male? a. 20/45 b. 15/35 c. 35/80 d. 15/80 160. The probability of an impossible event is 0. a. True b. False 161. A tree diagram has two levels. The first level has 3 branches, and the second level has 4 branches per branch of the first level. How many total outcomes are there? a. 24 b. 7 c. 27 d. 12 162. The probability of getting a number greater than 4 when a dice is thrown once is 1/3. a. False b. True 163. A coin is tossed three times. The number of possible outcomes is ____. a. 16 b. 3 c. 6 d. 8 164. If A and B are independent, then P(A∣B) _________. a. equals to P(A)×P(B) b. equals to P(B) c. equals to P(A) d. cannot be determined 165. If the probability of an event is 0.7, what is the probability of its complement? a. 0 b. 1.0c. 0.7 d. 0.3 166. A contingency table shows that 40 students play basketball, 30 play soccer, and 10 play both sports. What is the total number of students who play either sport? a. 60 b. 50 c. 70 d. 40 167. A contingency table displays the frequency distribution of two categorical variables. a. True b. False 168. In a survey, 50 people prefer tea, 40 prefer coffee, and 10 prefer both. Using a contingency table, what is the probability of choosing someone who prefers only coffee? a. 0.4 b. 0.3 c. 0.1 d. 0.5 169. In a small village, one bus arrives a day. Complete the tree diagram. a. a=0.15, b=0.4 b. a=0.3, b=0.7 c. a=0.4, b=0.15 d. a=0.6, b=0.85 170. In a school only, 3 out of 5 students can participate in a competition. What is the probability of the students who do not make it to the competition? a. 0.45 b. 0.4 c. 0.6 d. 0.65 171. Which of the following is true about probabilities?a. Probabilities can be negative b. Probabilities cannot equal 0 c. Probabilities are always between 0 and 1, inclusive d. Probabilities can exceed 1 172. What does a Venn diagram represent? a. The flow of data in a process b. The relationship between different sets c. The frequency of an event over time d. The relationship between numerical data and its mean 173. A contingency table is used to display the __________ distribution of two categorical variables. a. frequency b. data c. time d. years 174. If P(A) = 0.4 and P(B) = 0.5, and A and B are mutually exclusive, P(A∪B) is _____. a. 1.0 b. 0.9 c. 0.1 d. 0.2 175. In a contingency table, if there are 100 total observations, 60 belong to A, 40 belong to B, and 20 belong to both A and B, what is P(A∪B)? a. 0.8 b. 0.7 c. 0.6 d. 0.4 176. Listed here are the temperatures in °C for 10 days: –6, –8, 0, 3, 2, 0, 1, 5, 4, 4. What is the range of the data? a. 13 °C b. 10 °C c. 8 °C d. 12 °C 177. A coin tossed two times, the probability of at least one head to show is______. a. 3/4 b. 1/4 c. 1/2 d. 1 178. A spinner has green sections and blue sections. The probability of the spinner landing on green is 2/7. The spinner is spun twice. Using the tree diagram, work outthe probability of the spinner landing on green twice. a. 4/49 b. 2/7 c. 5/7 d. 4/14 179. A bag contains 4 red balls and 5 blue balls. Raheem picks 2 balls at random. Use the tree diagram to determine the probability of selecting the same color twice. a. 20/72 b. 12/72 c. 32/72 d. 240/72 180. Two dice are rolled. What is the probability that the sum of the numbers is 7? a. 6/36 b. 1/36 c. 7/36 d. 2/6 181. What does the overlapping area in a Venn diagram represent? a. The intersection of two events. b. Mutually exclusive events. c. The union of two events. d. The complement of two events.182. In a binomial experiment, the trials are dependent on each other. a. True b. False 183. If the probability of success is 0.6 in a binomial distribution, the probability of failure is: a. 0.2 b. 0.4 c. 1.0 d. 0.6 184. The variance of a random variable is always a non-negative value. a. True b. False 185. A lacrosse team is selecting a captain. The names of all the seniors are put into a hat, and the first three that are drawn will be the captains. The names are not replaced once they are drawn (one person cannot be two captains). You want to see if the captains all play the same position. Is this a binomial distribution? State why or why not. a. Yes, because there are two possible outcomes for each draw: either the person plays the same position or not. b. No, because the names are not replaced after each draw, which means the trials are not independent. c. No, because the number of trials is greater than two. d. Yes, because the trials are independent, and there are only two outcomes for each trial. 186. For a fair die roll, the expected value of the outcome is: a. 4 b. 3.5 c. 6 d. 5.5 187. The probability that a professional poker player wins a hand in a tournament is 0.42, based on past performance over 500 hands played. In an upcoming tournament, the player is expected to play 15 hands. What is the expected number of hands the player will win during the tournament? a. 6 b. 7 c. 6.3 d. 5.5 188. If P(X=x)=0 for a value of x, which of the following statements is true? a. The event is undefined b. The event is impossiblec. The event is likely d. The event is certain 189. A basketball team has the following probabilities for winning a game: win (0.7), loss (0.2), tie (0.1). What is the expected number of wins for the team in 5 games? a. 3.5 b. 7 c. 1 d. 2.5 190. If the mean of X is 12, the mean of 2X+3 is: a. 27 b. 12 c. 15 d. 24 191. For a binomial distribution, if p=0.3 and n=15, the variance is: a. 4.5 b. 3.15 c. 2.1 d. 5 192. Assume that the pair of dice is thrown, and the random variable X is the sum of numbers that appear on two dice. Find the expectation of the random variable X. a. 7 b. 6 c. 5 d. 8 193. The expected value E(X) of a random variable X is also known as the __________ of X. a. standard deviation b. variance c. median d. mean 194. If a PDF is given by P(X=x) for a random variable X, then which of the following is always true? a. 0 leqP(X=x) leq1 b. P(X=x)≥1 c. P(X=x)1 d. P(X=x)0 195. A binomial experiment consists of a fixed number of _____. a. events b. probabilities c. outcomesd. trials 196. If a die is rolled, and X represents the outcome of the roll, what is the probability that X is a prime number? a. 0.33 b. 0.5 c. 0.66 d. 0.17 197. The lifetime risk of developing a particular disease is about one in 67 (1.5%). Suppose we randomly sample 200 people. Let X = the number of people who will develop the disease. What is the probability distribution for X? a. N(200,0.015) b. B(200,0.015) c. P(200,0.015) d. U(200,0.015) 198. In a city, 70% of households have internet access. If 8 households are surveyed, what is the probability that exactly 6 have internet access? a. 0.5292 b. 0.4420 c. 0.2965 d. 0.3678 199. If P(X=2) = 0.3, P(X=3) = 0.5, and P(X=4) = 0.2, what is P(X≥3)? a. 0.2 b. 0.5 c. 0.3 d. 0.7 200. Suppose Nancy has classes three days a week. She attends classes three days a week 80% of the time, two days 15% of the time, one day 4% of the time, and no days 1% of the time. Suppose one week is randomly selected. Let X = the number of days Nancy attends class per week. What values does X take on? a. 1, 2, 3, 4 b. 1, 2, 3 c. 0, 1, 2, 3, 4 d. 0, 1, 2, 3 201. A fair coin is tossed 3 times. The probability of getting at least one head is: a. 1 b. 0.875 c. 0.125 d. 0.5 202. The formula for the variance of a discrete random variable X is:a. b. c. d. 203. The monthly income of a group of 100 employees is normally distributed with a mean of $3,500 and a standard deviation of $400. What is the expected total income of all employees? a. $330,000 b. $340,000 c. $350,000 d. $370,000 204. The probability of getting exactly 3 successes in 10 trials when p=0.2 is: a. b. c. d. 205. Which of the following is an example of a discrete random variable? a. The number of heads in 5 coin tosses b. The speed of a car c. The time it takes to run a mile d. The height of 5 students in a class of 10 206. For a valid discrete probability distribution, the sum of all probabilities must be _____. a. 0 b. 1 c. less than 1 d. greater than 1207. If the probability of an event occurring is P(A)=0.6 and P(B)=0.7, what is the probability of the event B not occurring? a. 0 b. 0.6 c. 0.3 d. 0.4 208. For a random variable X, E(X)=10 and Var(X)=4. What is E(X^2)? a. 6 b. 104 c. 14 d. 96 209. The mean of a probability distribution can be a value not in the sample space. a. False b. True 210. The probability of an event can be infinite. a. True b. False 211. If all the values in a dataset are identical, what is the variance of the dataset? a. Undefined b. Infinite c. 1 d. 0 212. The probability of any specific value of a discrete random variable is always positive. a. True b. False 213. A probability distribution function for a discrete random variable lists the values and their corresponding _____. a. probabilities b. variances c. ratios d. averages 214. The Poisson distribution is appropriate when the events are rare or infrequent. a. True b. False 215. In a Poisson distribution, the mean and variance are both equal to 1. a. True b. False216. For a population of 80 items with 30 defective items, and a sample size of 12, the variance of the hypergeometric distribution is __________. a. 3.4 b. 5.2 c. 6.8 d. 2.4 217. If the average rate of occurrence λ is 3 events per hour, the probability of observing exactly 2 events in one hour is __________. a. 0.224 b. 0.100 c. 0.224 d. 0.149 218. In a population of 100 items, 40 are defective, and a sample of 10 items is drawn. What is the probability of selecting exactly 3 defective items from the sample using the hypergeometric distribution? a. 0.220 b. 0.198 c. 0.215 d. 0.149 219. If the probability of success is 0.2, the probability of failure on the first trial is __________. a. 0.4 b. 0.6 c. 0.2 d. 0.8 220. The Poisson distribution can be used to model which of the following situations? a. The probability of getting 5 heads when flipping a fair coin 10 times. b. The height of individuals in a population. c. The number of phone calls received at a call center in 1 hour. d. The number of defective items in a batch of 100. 221. Calculate the mean and variance for a Poisson distribution with λ = 5. a. Mean = 5, Variance = 5 b. Mean = 5, Variance = 0 c. Mean = 5, Variance = 10 d. Mean = 10, Variance = 5 222. In the Poisson distribution, when λ is very large, the distribution begins to resemble __________. a. a uniform distribution. b. a normal distribution. c. a binomial distribution.d. a geometric distribution. 223. When does a Poisson distribution approximate a binomial distribution? a. When n is small b. When λ is large and n is large c. When λ is small and n is large, with p being small d. When λ is equal to n 224. If the Poisson distribution models the number of customers arriving at a store, what is the relationship between the mean and variance? a. Mean Variance b. Mean Variance c. Mean = Variance d. Mean and variance are unrelated. 225. The Poisson distribution is appropriate for modelling the heights of a group of people. a. True b. False 226. The variance of a geometric distribution with probability of success p is given by the formula (1-p)/p^2. a. True b. False 227. The Hypergeometric distribution is most appropriate for modeling the number of heads obtained from 10 flips of a fair coin. a. True b. False 228. In a factory, the probability of producing a defective item is 0.05. What is the probability that the first defective item is produced on the 3rd item? a. 0.0287 b. 0.0451 c. 0.1361 d. 0.8575 229. The Hypergeometric distribution is used to model: a. The number of trials needed to get the first success. b. The number of successes in a fixed number of trials without replacement. c. The number of successes in a fixed number of independent trials with replacement. d. The number of events occurring in a fixed interval of time. 230. In a Poisson distribution, what does the parameter λ represent? a. The mean of the distribution. b. The variance of the distribution.c. The number of trials. d. The number of events in a fixed time interval. 231. For a game where the probability of scoring is 0.3, what is the probability of scoring for the first time on the 4th attempt? a. 0.1029 b. 0.1156 c. 0.0729 d. 0.2401 232. The Poisson distribution is characterized by ____________. a. a normal distribution curve. b. a fixed probability of success in each trial. c. a parameter λ (lambda), which represents the average number of events. d. a fixed number of trials. 233. The variance of a geometric distribution is given by σ^2=(1-p)/p^2. If p=0.5, what is the variance? a. 0.5 b. 1 c. 4 d. 2 234. For a Poisson distribution, how does the shape of the distribution change as the rate parameter λ increases? a. It becomes more skewed to the left. b. It stays the same. c. It becomes more skewed to the right. d. It becomes more symmetrical. 235. The Geometric distribution models the probability of ____________. a. the number of successes in a fixed number of trials. b. the probability of observing a specific outcome in a fixed number of trials. c. the number of events occurring in a fixed interval of time. d. the number of trials until the first success. 236. The trials in a geometric distribution are dependent. a. False b. True 237. The Poisson distribution is often used to model _____________ . a. the number of heads in a coin toss. b. the number of customers arriving at a service center. c. the amount of money spent by a customer. d. the probability of getting a certain score on a test.238. In a hospital, the average number of patients arriving in an emergency room per hour is 4. What is the probability of receiving exactly 2 patients in the next hour? a. 0.1345 b. 0.1465 c. 0.1822 d. 0.1954 239. The mean of a geometric distribution is given by μ=1/p. If p=0.25, what is the mean? a. 4 b. 0.25 c. 5 d. 0.75 240. If the probability of success on each trial is p=0.6, what is the expected number of trials needed to get the first success? a. 2 b. 1.67 c. 3 d. 0.6 241. A Poisson distribution with λ = 2 is used to model the number of customers arriving at a store per minute. What is the probability of 1 customer arriving in the first minute? a. b. c. d. 242. In a Geometric distribution, if the probability of success on a single trial is p=0.4, what is the probability that the first success occurs on the 3rd trial? a. b. c.d. 243. What is the probability of having more than 5 events (X 5) in a Poisson distribution with λ = 4? a. P(X5) = 1 - P(X≤5) b. P(X5) = P(X=5) c. P(X5) = 1 - P(X≥5) d. P(X5) = 1 - P(X=5) 244. If a population has 20 items (8 good and 12 bad), what is the probability of getting exactly 2 good items when selecting 4? a. 0.200 b. 0.220 c. 0.382 d. 0.180 245. The expected value (mean) of a Geometric distribution with parameter p is ____________. a. b. c. d. p 246. For the graph below, find the probability that x falls in the shaded area. Select one: a. 0.6 b. 0.5 c. 0.625 247. A call center technical specialist spends varying amount of time in each call to resolve the concern. The time spent in each call is modeled using the following distribution: X ~ Exp(0.2). Find the 70th percentile. Select one: a. 6.02 b. 5.02 c. 2.02248. A call center technical specialist spends varying amount of time in each call to resolve the concern. The time spent in each call is modeled using the following distribution: X ~ Exp(0.2). Find the 50th percentile (or median). Select one: a. 2.44 b. 3.00 c. 3.47 249. Let X be a binomial random variable with probability of success 0.22. The number of successes is obtained in 21 independent trials. Find the variance of X. Select one: a. 3.6 b. 1.9 c. 13 250. Which type of distribution does the graph illustrate? Select one: a. Binomial distribution b. Uniform distribution c. Exponential distribution 251. A coin is flipped once. Let X the random variable representing the two possible outcomes with the following probability distribution. What is the expected value of X? Select one: a. 0.5 b. 0 c. 0.25 252. A call center technical specialist spends varying amount of time in each call to resolve the concern. The time spent in each call is modeled using the following distribution: X ~ Exp(0.2). Find P(x 6). Select one: a. 0.01012 b. 0.3012 c. 0.062253. For the graph below, find the probability that x falls in the shaded area: a. 0.333 b. 0.222 c. 0.455 254. For a continuous probability distribution, 0 ≤ x ≤ 10. What is P (x = 7)? a. 0.75 b. 0 c. .33 255. A call center technical specialist spends varying amount of time in each call to resolve the concern. The time spent in each call is modeled using the following distribution: X~ Exp (0.2). Find P (2 x 10): a. 0.5350 b. 0.6350 c. 0.2350 256. A call center technical specialist spends varying amount of time in each call to resolve the concern. The time spent in each call is modeled using the following distribution: X~ Exp (0.2). What is the standard deviation? a. 3 b. 2 c. 5 257. What is the area under f(x) if the function is a continuous probability density function? a. 1.0 b. 2.5 c. 1.5 258. What does the shaded area represent? P (___ x ___) a. P (2 x 5) b. P (1 x 8) c. P (5 x 8)259. A coin is flipped once. Let X the random variable representing the two possible outcomes with the following probability distribution. What is the standard deviation of X? Select one: a. 0.50 b. 0.00 c. 0.707 260. A continuous probability function is restricted to the portion between x = 0 and 7. What is P (x = 10)? a. 0 b. .99 c. .05 261. On a multiple-choice final exam with 20 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers: a. 10 questions b. 4.3 questions c. 5.0 questions 262. For a continuous probability distribution, 0 ≤ x ≤ 15. What is P (x 15)? a. 0.25 b. 1 c. 0 263. A coin is flipped once. Let X the random variable representing the two possible outcomes with the following probability distribution. What type of random variable represents X? Select one: a. a continuous random variable b. a discrete random variable 264. Which type of distribution does the below graph illustrate?a. binomial distribution b. uniform distribution c. exponential distribution 265. Let X a binomial random variable with the probability of success of 0.22. The number of successes is obtained in 21 independent trials. Find the expected value of X: a. 1.9 b. 4.62 c. 2.6 266. The summary statistics for a paired data set is provided below. Compute the standard error (SE) associated with