1.) 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) = 199 and standard deviation SD(X) = 293.4. Since the possible values of Xare only integers and since the distribution of X is highly skewed to the right, the distribution of X cannot be described by a normal model. Suppose you select a random sample of 30 Facebook users and record the number of Facebook friends each user has.
a.) What is the probability that the 30 Facebook users in your sample have a sample mean number of friends x¯ greater than 204?____ (use 4 decimal places in your answer)
b.) What is the probability that the 30 Facebook users in your sample have a sample mean number of friends x¯ less than 218?_____ (use 4 decimal places in your answer)
2.) The National Center for Education Statistics reports that the proportion of college freshmen who return to the same school for their sophomore year is 0.66. Suppose we select a random sample of 430 freshmen from across the nation.
a.) What is the expected value of the sampling distribution model for the proportion of 430 freshmen that will return to the same school for their sophomore year? ______
b.) What is the standard deviation of the sampling distribution model for the proportion of 430 freshmen that will return to the same school for their sophomore year? ______ (round to 3 decimal places)
c.) What is the probability that the proportion of these 430 freshmen that return to the same school for their sophomore year is less than 0.72? ______ (round to 4 decimal places)
3.) Just before a city referendum on a school budget, a local newspaper polls 400 voters in an attempt to predict whether the budget will pass. Suppose that, unknown to everyone, the budget actually has the support of 56% of the voters.
a.) 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 p^ less than 0.50 in favor of the referendum? ______ (calculate the standard deviation of p^ to 4 decimal places, round your final answer to 4 decimal places).