An exhaustive study of all active Facebook accounts was recently conducted by Fa

Question

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) = 292. 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 33 Facebook users and record the number of Facebook friends each user has.

Question 1. What is the probability that the 33 Facebook users in your sample have a sample mean number of friends x greater than 208?

(use 4 decimal places in your answer)

Question 2. What is the probability that the 33 Facebook users in your sample have a sample mean number of friends x less than 220?

(use 4 decimal places in your answer)

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

true/ false

Explanation / Answer

Solution:- Given that E(X) = 199 and standard deviation SD(X) = 292

1) For n = 33

P(x > 208) = P((x - ?)/(?/sqrt(n)) > (208 - 199)/(292/sqrt(33))

= P(Z > 0.1771)

= 1 ? P(Z < 0.1771)

= 1 ? 0.5714

= 0.4286

2) For n = 33

P(X < 220) =  P((x - ?)/(?/sqrt(n)) < (220 - 199)/(292/sqrt(33))

= P(Z < 0.4131)

= 0.6591

3) option A. True.

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