Question

A 2014 Pew study found that the average US Facebook user has 338 friends. The study also found that the median US Facebook user has 200 friends. The Pew study did not report a standard deviation, but given the number of Facebook friends is highly variable, let's suppose that the standard deviation is 194. Let's also suppose that 338 and 194 are population values (they aren't, but we don't know the true population values so this is the best we can do). (Use 3 decimal place precision for parts a., b., and c.) a. If we randomly sample 108 Facebook users, what is the probability that the mean number of friends will be less than 343? b. If we randomly sample 115 Facebook users, what is the probability that the mean number of friends will be less than 311? c. If we randomly sample 500 Facebook users, what is the probability that the mean number of friends will be greater than 343? (Round to the nearest integer for parts d. and e.) d. If we repeatedly take samples of n=500 Facebook users and construct a sampling distribution of mean number of friends, we should expect that 95% of sample means will lie between and e. The 75th percentile of the sampling distribution of mean number of friends, from samples of size n=108, is:

Answer 1