At supermarkets 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

μ=75 cents and standard deviation σ = 5 cents. That is PRICE ~ N(75,5).

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

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

iii) Find the probability that more than 6300 cans are sold per week. Draw a sketch to

illustrate your calculation.