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.

Question 1. 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)

Question 2. 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)

Question 3. The Central Limit theorem was needed to answer questions 1 and 2 above.

True OR False??