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) = 187 and standard deviation SD(X) = 283.6. 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 168?

(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 197?

(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?   

Answer 1

Solution :

Given that,

mean = = 187

standard deviation = = 283.6

n = 35

= = 187

= / n = 283.6/ 35 = 47.94

1) P( > 168) = 1 - P( <168 )

= 1 - P[( - ) / < (168 - 187) / 47.94 ]

= 1 - P(z < -0.40)

Using z table,    

= 1 - 0.3446

= 0.6554

2) P( < 197) = P(( - ) / < (197 - 187) / 47.94 )

= P(z < 0.21)

Using z table

= 0.5832

3) True , because sample size is greater than 30.