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) What is the mean and standard deviation of the number of Facebook posts "liked" in a whole year?

(b) 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) 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) Are you sure?

Recall that in the previous problem set each student in the course received a different random sample of two observations drawn from the Standard Normal distribution; you can find your sample at the following link: https://tinyurl.com/ e2kvjn7n.

(a) Assume you don't know the population mean, but you know that the population standard deviation is 1. Calculate the 95% confidence interval for the population mean using the sample mean of your individual sample. You will report the confidence interval in the Pre-lecture 6 quiz.

(b) Assume that all 189 students in the course calculated the 95% confidence intervals correctly based on the sample mean of their individual sample. How many of their confidence intervals do you expect will miss the true value of the population mean?