1. The number of customers arriving at a restaurant is Poisson distributed with a mean of 15 per hour. The amount that each customer spends is exponentially distributed with an average of 20. The restaurant is open 16 hours each day and the daily expenses are 4500. Using a normal approximation, estimate the probability that on a given day, revenue will cover expenses.

2. Suppose that N is a continuous mixture of Poisson distributions where the mean is itself a random variable. Find P(N = 0) in each of the following cases.

(a) The mean is uniformly distributed on the interval [1, 3].

(b) The mean has a Gamma (2, 3) distribution.