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) = 191 and standard deviation SD(X) = 287.9. Since the possible values of X are 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 35 Facebook users and record the number of Facebook friends each user has.

**Question 1. **What is the probability that the 35 Facebook users in your sample have a sample mean number of friends x greater than 213?

(use 4 decimal places in your answer)

**Question 2.** What is the probability that the 35 Facebook users in your sample have a sample mean number of friends x less than 182?

(use 4 decimal places in your answer)

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

True

False