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 )_( between 6.57 and 6.97. -.2685 3' (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 )_( 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 False V '4 Points] DETAILS PREVIOUS ANSWERS ' MY NOTES The heights of European 13-year-old boys can be approximated by a normal model with mean y of 63.1 inches and standard deviation 0' 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 )_( 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 )_( is greater than 65.6 inches? (use 4 decimal places in your answer) 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 ofX are only integers and since the distribution ofX is highly skewed to the right, the distribution of X 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. : Question 2. : Question 3. True False J 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) 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) The Central Limit theorem was needed to answer questions 1 and 2 above