At supermarkets sales of "Chicken of the Sea" canned tuna vary from week to week. Marketing researchers have determined that there is a relationship between sales of canned tuna and the price of canned tuna. Specifically, SALES \(=50000-100\) PRICE. SALES is measured as the number of cans per week and PRICE is measured in cents per can. Suppose PRICE over the year can be considered (approximately) a normal random variable with mean \(\mu=248\) cents and standard deviation \(\sigma=10\) cents.

a. Find the expected value of SALES.

b. Find the variance of SALES.

c. Find the probability that more than 24,000 cans are sold in a week. Draw a sketch illustrating the calculation.

d. Find the PRICE such that SALES is at its 95th percentile value. That is, let \(S A L E S_{0.95}\) be the 95th percentile of \(S A L E S\). Find the value \(P R I C E_{0.95}\) such that \(P\left(S A L E S>S A L E S_{0.95}\right)=0.05\).