Question

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 113 and a standard deviation of about 43. Assume forty individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
2. For the group of 40, find the probability that the average number of friends is more than 119.
3. Find the first quartile for the average number of Facebook friends.
4. For part b), is the assumption that the distribution is normal necessary? Yes No

Answer 1

d) No, since sample size is large enough ( > 30), so we can approximate the probability distribution of sample mean by normal distribution, using Central limit theorem.