1.) An exhaustive study of all active Facebook accounts was recently conducted by Facebook. One variable Facebook recorded was the number of friendsXof each Facebook user. SupposeXhas expected value E(X) =199and standard deviation SD(X) =293.4. Since the possible values ofXare only integers and since the distribution ofXis highly skewed to the right, the distribution ofXcannotbe described by a normal model. Suppose you select a random sample of30Facebook users and record the number of Facebook friends each user has.

a.) What is the probability that the30Facebook users in your sample have a sample mean number of friendsxgreater than204?

_____ (use 4 decimal places in your answer)

b.) What is the probability that the30Facebook users in your sample have a sample mean number of friendsxless than218?

_____ (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 is0.66. Suppose we select a random sample of430freshmen from across the nation.

a.) What is the expected value of the sampling distribution model for the proportion of430freshmen 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 of430freshmen 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 these430freshmen that return to the same school for their sophomore year is less than0.72?

______ (round to 4 decimal places)

3.) Just before a city referendum on a school budget, a local newspaper polls400voters in an attempt to predict whether the budget will pass. Suppose that, unknown to everyone, the budget actually has the support of56% 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 proportionpless than 0.50 in favor of the referendum?

______ (calculate the standard deviation ofpto 4 decimal places, round your final answer to 4 decimal places).