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 207. Let's also suppose that 338 and 207 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 119 Facebook users, what is the probability that the mean number of friends will be less than 345?  
b. If we randomly sample 102 Facebook users, what is the probability that the mean number of friends will be less than 310?  
c. If we randomly sample 400 Facebook users, what is the probability that the mean number of friends will be greater than 345?