A large retail chain sends out an ad about a new product to 15 million users on Facebook and asks them to like the message. Assume the probability that a user will like the message (instead of ignoring it) is 0.00001.
a. State assumptions for a binomial distribution to apply for X = the number of likes the message will receive. Identify n and p for that distribution.
b. Suppose the assumptions are met. Find the mean and standard deviation of X.
c. Is it reasonable to approximate the binomial distribution with the normal one? Why? (Assume the assumptions are met.)
d. Based on the normal approximation of the binomial distribution, find the interval for the possible numbers of likes that are within three standard deviations of the mean.