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) = 180 and standard deviation SD(X) = 280.7. 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.

A) What is the probability that the 35 Facebook users in your sample have a sample mean number of friends x greater than 177?

(use 4 decimal places in your answer)

B) What is the probability that the 35 Facebook users in your sample have a sample mean number of friends x less than 183?

(use 4 decimal places in your answer)

Answer 1

Solution :

Given that ,

mean = = 180

standard deviation = = 280.7

= / n = 280.7 / 35 = 47.4470

A)

P( > 177) = 1 - P( < 177)

= 1 - P[( - ) / < (177 - 180) / 47.4470]

= 1 - P(z < -0.06)

= 1 - 0.4761

= 0.5239

Probability = 0.5239

B)

P( < 183) = P(( - ) / < (183 - 180) / 47.4470)

= P(z < 0.06)

= 0.5239

Probability = 0.5239