MATH 225N Statistics Final EXAM Chamberlain College of Nursing MATH 225N 2026/2027

MATH 225N Statistics Final EXAM Chamberlain College of Nursing MATH 225N 2026/2027 1. Solve the problem. In the game of craps two dice are rolled and the up faces are totaled. If the person rolling the dice on the first roll rolls a 7 or an 11 total they win. If they roll a 2, 3, or 12 on the first roll they lose. If they roll any other total then on subsequent rolls they must roll that total before rolling a 7 to win. What is the probability of winning on the first roll? - ANSWER 0.22 2. Suppose a basketball player is an excellent free throw shooter and makes 91% of his free throws (i.e., he has a 91% chance of making a single free throw). Assume that free throw shots are independent of one another. Suppose this player gets to shoot four free throws. Find the probability that he misses all four consecutive free throws. Round to the nearest ten thousandth. - ANSWER 0.0001 3. Provide an appropriate response. A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}. Find the probability of getting two numbers whose sum is less than 13. - ANSWER 1 4. The complement of 4 heads in the toss of 4 coins is - ANSWER at least one tail. 5. How many distinct arrangements can be formed from all the letters of "students"? - ANSWER 10,080 6. A human gene carries a certain disease from the mother to the child with a probability rate of 57%. That is, there is a 57% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has four children. Assume that the infections of the four children are independent of one another. Find the probability that at least one of the children get the disease from their mother. Round to the nearest thousandth. - ANSWER 0.966 7. In a carnival game, a person wagers $2 on the roll of two dice. If the total of the two dice is 2, 3, 4, 5, or 6 then the person gets $4 (the $2 wager and $2 winnings). If the total of the two dice is 8, 9, 10, 11, or 12 then the person gets nothing (loses $2). If the total of the two dice is 7, the person gets $0.75 back (loses $0.25). What is the expected value of playing the game once? - ANSWER $-0.04 8. Provide an appropriate response. The produce manager at a farmer's market was interested in determining how many oranges a person buys when they buy oranges. He asked the cashiers over a weekend to count how many oranges a person bought when they bought oranges and record this number for analysis at a later time. The data is given below in the table. The random variable x represents the number of oranges purchased and P(x) represents the probability that a customer will buy x apples. Determine the mean number of oranges purchased by a customer. - ANSWER 3.97 9. Provide an appropriate response. The sum of the probabilities of a discrete probability distribution must be - ANSWER equal to one 10. A random variable is - ANSWER a numerical measure of the outcome of a probability experiment. 11. Assume that the random variable X is normally distributed, with mean and standard deviation Compute the probability P(57 X 105). - ANSWER 0.8914 12. The amount of corn chips dispensed into a 32-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 32.5 ounces and a standard deviation of 0.2 ounce. What chip amount represents the 67th percentile for the bag weight distribution? Round to the nearest hundredth. - ANSWER 32.59 13. Furnace repair bills are normally distributed with a mean of 269 dollars and a standard deviation of 30 dollars. If 144 of these repair bills are randomly selected, find the probability that they have a mean cost between 269 dollars and 271 dollars. - ANSWER 0.2881 14. High temperatures in a certain city for the month of August follow a uniform distribution over the interval 69 to 87 What is the probability that a randomly selected August day has a high temperature that exceeded - ANSWER 0.7222 15. The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standard deviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability that the mean daily revenue for the next 30 days will exceed $7000? - ANSWER 0.1814 16. Suppose a population has a mean of 7 for some characteristic of interest and a standard deviation of 9.6. A sample is drawn from this population of size 64. What is the standard error of the mean? - ANSWER 1.2 17. Assume that blood pressure readings are normally distributed with a mean of 122 and a standard deviation of 9.6. If 144 people are randomly selected, find the probability that their mean blood pressure will be less than 124. - ANSWER 0.9938 18. A researcher wishes to estimate the number of households with two computers. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 6%? A previous study indicates that the proportion of households with two computers is 23%. - ANSWER 268 19. The principal at Riverside High School would like to estimate the mean length of time each day that it takes all the buses to arrive and unload the students. How large a sample is needed if the principal would like to assert with 90% confidence that the sample mean is off by, at most, 7 minutes. Assume σ = 14 minutes. - ANSWER 11 20. In a random sample of 60 dog owners enrolled in obedience training, it was determined that the mean amount of money spent per owner was $109.33 per class. Assuming the population standard deviation of the amount spent per owner is $12, construct and interpret a 95% confidence interval for the mean amount spent per owner for an obedience class. - ANSWER ($106.29, $112.37); we are 95% confident that the mean amount spent per dog owner for a single obedience class is between $106.29 and $112.37.