4. The mean number of posts a person "likes" on Facebook per month is 311.11, with a standard deviation of 72.42. The number of posts "liked" on Facebook per month can only take integer values, so the distribution of "likes given" is not Normal. (a) (4 points) What is the mean and standard deviation of the number of Facebook posts "liked" in a whole year?

(b) (6 points) You sample a person's Facebook profile activity for every month for the last 5 years. What are the chances that the average number of posts "liked" per month in your sample is larger than 307? (c) (5 points) Suppose you don't know the mean number of Facebook posts "liked", but still know the standard deviation is 72.42. You would like to calculate a 90% confidence interval for the mean number of posts "liked" per month. What is the smallest number of months you will have to sample if you'd like your confidence interval to have a margin of error no larger than 27?

(d) (2 points) Are you sure?