STA2023 Exam 2

STA2023 Exam #2 Sean is collecting data on lap swim time. What type of data is this? The table below shows a probability density function for a discrete random variable X, the number of coffee cups an employee brews at an office coffee machine per day. What is the probability that X is 3?Provide the final answer as a fraction. A casino features a game in which a weighted coin is tossed several times. The table shows the probability of each payout amount. To the nearest dollar, what is expected payout of the game? A random sample of math majors taking an introductory statistics course were surveyed after completing the final exam. They were asked, "How many times did you review your final exam before handing it in to the professor?" The results are displayed in a probability density function for the random variable X, the number of times students reviewed their exam before handing it in. Find the standard deviation of X. Round the final answer to two decimal places. Identify the parameter p in the following binomial distribution scenario. A basketball player has a 0.463 probability of making a free throw and a 0.537 probability of missing. If the player shoots 17 free throws, we want to know the probability that he makes no more than 6 of them (consider made free throws as successes in the binomial distribution). Do not include p in your answer. Given the plot of normal distributions A, B and C below, which of the following statements is true? Select all correct answers. Hugo averages 59 words per minute on a typing test with a standard deviation of 10.5 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then X∼N(59,10.5). After collecting the data, Maria finds that the number of points per game for a certain basketball player is normally distributed with mean 14 points and standard deviation 2 points. Based on the Empirical Rule, what is the probability that in a randomly selected game, the player scored less than 8 points? Enter your answer as a percent rounded to 2 decimal places if necessary. Determine the area under the standard normal curve that lies to the right of the z-score 0.05 and to the left of the z-score 0.25. The pages per book in a library have an unknown distribution with mean 290 and standard deviation 24 pages. A sample, with size n=55, was randomly drawn from the population. Using the Central Limit Theorem for Means, what is the mean for the sample mean distribution? Suppose the number of inches of rainfall each year in a city is normally distributed. For a random sample of years, the confidence interval (3.9,7.7) is generated. Find the margin of error. Suppose we know that a confidence interval for a population mean is (29,37), with a margin of error of 4. What is the sample mean? The number of square feet per house are normally distributed with a population standard deviation of 137 square feet and an unknown population mean. A random sample of 19 houses is taken and results in a sample mean of 1350 square feet. Find the margin of error for a 80% confidence interval for the population mean. Round the final answer to 2 decimal places. The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 1 inch of the true population mean, what is the minimum sample size that can be taken? The lengths, in days, of job searches for individuals making career transitions are normally distributed with an unknown population mean and standard deviation. If a random sample of 45 career changers is taken to estimate the mean job search length, what t-score should be used to find a 99% confidence interval estimate for the population mean? Juan wants to estimate the percentage of people who will vote for issue A on the next election. He surveys 150 individuals and finds that 81 will vote for issue A. Find the margin of error for the confidence interval for the population proportion with a 90% confidence level. A clothing store wants to determine the current percentage of customers who are over the age of forty. The store wants to create a 98% confidence interval which has a margin of error of at most 2%. How many customers should be polled to create this confidence interval? In a large population, about 10% of people do not like the taste of cilantro, an herb used in cooking. A researcher takes a random sample of 15 people and surveys whether they like cilantro. Use the binomial distribution to compute the probability that exactly 6 of the people in the sample do not like cilantro. Identify the following information required to find the probability of people who do not like the taste of cilantro. The lengths of text messages are normally distributed with a population standard deviation of 3 characters and an unknown population mean. A random sample of 24 text messages is taken and results in a sample mean of 27 characters. Identify the parameters needed to calculate a confidence interval at the 95% confidence level. Then find the confidence interval. Round the final answer to one decimal place, if necessary. Suppose that the ages of investors in a a particular mutual fund are normally distributed with an unknown mean and standard deviation. A random sample of 22 investors is taken and gives a sample mean of 43 years old and a sample standard deviation of 5 years. Use the portion of the table above. Round the final answer to two decimal places. Eric wants to estimate the percentage of elementary school children who have a social media account. He surveys 450 elementary school children and finds that 280 have a social media account. Identify the values needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval. Round the final answer to three decimal places.