At supermarkets in a Midwestern city the sales of canned tuna varies 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 = 40710

- 430PRICE where SALES are cans sold 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 75 cents and standard deviation 5 cents. That is

PRICE ~ N(75, 25).

(a) What is the numerical expected value of SALES? Show your work.

(b) What is the numerical value of the variance of SALES? Show your work.

(c) Find the probability that more than 6,300 cans are sold in a week. Draw a sketch

illustrating the calculation.