The Nationa Center for Education Statistics reports that the proportion of college freshmen who return to the same school for their sophomore year is 0.67. Suppose we select a random sample of 500 freshmen from across the nation. Question 1. What is the expected value of the sampling distribution model for the proportion of 500 freshmen that will return to the same school for their sophomore year? 0.67 Question 2. What is the standard deviation of the sampling distribution model for the proportion of 500 freshmen that will return to the same school for their sophomore year? .022 x (Round to 3 decimal places) Question 3. What is the probability that the proportion of these 500 freshmen that return to the same school for their sophomore year is less than 0.66? (Round to 4 decimal places) Submit Answer ' Just before a city referendum on a school budget, a local newspaper polls 410 voters in an attempt to predict whether the budget will pass. Suppose that, unknown to everyone, the budget actually has the support of 53% of the voters. Question. What is the probability the newspaper's sample will lead the newspaper to predict defeat of the referendum, that is, what is the probability that the newspaper's sample results in a sample proportion 13 less than 0.50 in favor of the referendum? (calculate the standard deviation off) to 4 decimal places, round your final answer to 4 decimal places). The distribution of weights of individual Starburst candies has mean )4 = 0.916 grams and standard deviation 0' = 0.036 grams. Let )7 denote the mean weight of the 29 Starburst candies in a package you have just purchased. Question 1. What is the expected value E()_() of the sampling distribution of )_(? grams Question 2. What is the standard deviation SD07) of the sampling distribution of )7? grams (use 6 decimal places) More than 100 million people around the world are not getting enough sleep; the average adult needs between 7.5 and 8 hours of sleep per night. College students are particularly at risk of not getting enough shut-eye. A recent survey of several thousand college students indicated that the total hours of sleep time per night, denoted by the random variable X, can be approximated by a normal model with E(X) = 6.83 hours and SD(X) = 1.14 hours. Question 1. Find the probability that the hours of sleep per night for a random sample of 4 college students has a mean )7 between 6.57 and 6.97. (use 4 decimal places in your answer) Question 2. Find the probability that the hours of sleep per night for a random sample of 16 college students has a mean )7 between 6.57 and 6.97. (use 4 decimal places in your answer) Question 3. Find the probability that the hours of sleep per night for a random sample of 25 college students has a mean )_( between 6.57 and 6.97. (use 4 decimal places in your answer) Question 4. The Central Limit Theorem was needed to answer questions 1, 2, and 3 above. True (9 False \\I \"4 Points] PREVIOUSANSWERS The heights of European 13-year-old boys can be approximated by a normal model with mean u of 63.1 inches and standard deviation 9' of 2.58 inches. Question 1. what is the probability that a randomly selected 13-year-old boy from Europe is taller than 65.6 inches? (use 4 decimal places in your answer) Question 2. A random sample of 4 European 13-year-old boys is selected. What is the probability that the sample mean height )7 is greater than 65.6 inches? (use 4 decimal places in your answer) Question 3. A random sample of 9 European 13-year-old boys is selected. What is the probability that the sample mean height )7 is greater than 65.6 inches? (use 4 decimal places in your answer) Question 4. The Central Limit Theorem was needed to answer questions 1, 2, and 3 above. True (9 False \\l 0. [14 Points] An exhaustive study of all active Facebook accounts was recently conducted by Facebook. One variable Facebook recorded was the number of friends X of each Facebook user. Suppose X has expected value E(X) = 200 and standard deviation SD(X) = 287. Since the possible values of X are only integers and since the distribution ofX is highly skewed to the right, the distribution ofX cannot be described by a normal model. Suppose you select a random sample of 32 Facebook users and record the number of Facebook friends each user has. Question 1. What is the probability that the 32 Facebook users in your sample have a sample mean number of friends )_( greater than 176? (use 4 decimal places in your answer) Question 2. What is the probability that the 32 Facebook users in your sample have a sample mean number of friends ; less than 223? (use 4 decimal places in your answer) Question 3. The Central Limit theorem was needed to answer questions 1 and 2 above. 0 True 0 False