A film-processing shop charges its customers 18 cents per print, but customers may refuse to accept one or more of the prints for various reasons. Assume that this shop does not charge its customers for refused prints. The number of prints refused per 24-print roll is a random variable with mean 1.5 and standard deviation 0.5.
a. Find the mean and standard deviation of the amount that customers pay for the development of a typical 24-print roll.
b. Assume that this shop processes 250 24-print rolls of film per week. Assuming the numbers of refused prints on these rolls are independent random variables, find the mean and standard deviation of the weekly film processing revenue of this shop.
c. Find an interval such that the manager of this film shop can be approximately 95% sure that the weekly processing revenue will be contained within the interval.