At a traveling carnival, a popular game is called the “Cash Grab.” In this game, participants step into a sealed booth, a powerful fan turns on, and dollar bills are dropped from the ceiling. A customer has 30 seconds to grab as much cash as possible while the dollar bills swirl around. Over time, the operators of the game have determined that the mean amount grabbed is $13 with a standard deviation of $9. They charge $15 to play the game and expect to have 40 customers at their next carnival.

a. What is the probability that an SRS of 40 customers grab an average of $15 or more?

b. How much should the operators charge if they want to be 95% certain that the mean amount grabbed by an SRS of 40 customers is less than what they charge to play the game?