Question 6.16

6.16 Number of friends on Facebook.

Facebook recently examined all active Facebook users (more than 10% of the global population) and determined that the average user has 190 friends. This distribution takes only integer values, so it is certainly not Normal. It is also highly skewed to the right, with a median of 100 friends.5 Suppose that and you take an SRS of 70 Facebook users.

  1. For your sample, what are the mean and standard deviation of , the mean number of friends per user?
  2. Use the central limit theorem to find the probability that the average number of friends for 70 Facebook users is greater than 250.
  3. What are the mean and standard deviation of the total number of friends in your sample? (Hint: For parts (c) and (d), use rules for means and variances for a sum of independent random variables found in Section 4.5, pages 226 and 231.)
  4. What is the probability that the total number of friends among your sample of 70 Facebook users is greater than 17,500?