Price of corn flakes cereal vary from week to week in supermarkets in Phoenix ar

Question

Price of corn flakes cereal vary from week to week in supermarkets in Phoenix area. Researchers have determined that there is a relationship between sales of corn flakes and the price of corn flakes. Specifically, SALES = 10,000-500*PRICE where SALES is boxes (12 OZ boxes) of corn flakes sold in a week and price is measured in dollars per box. Suppose PRICE over the past several years can be considered normally distributed with mean of $2 and standard deviation of 50 cents.
2a) What is the numerical expected value of SALES? Show your work.

2b) What is the numerical value of the variance of SALES?

2c) Find the probability that more than 9,250 boxes are sold in a week.

Explanation / Answer

2a)  numerical expected value of SALES =10000-500*E(Price) = 10000-500*2 =9000

2b) Varince of sales =5002*Var(price) =5002*(0.5)2 =62500

2c) here std deviation of sales =(62500)1/2 =250

hence probability that more than 9,250 boxes are sold in a week =P(X>9250) =1-P(X<9250)

=1-P(Z<(9250-9000)/250)=1-P(Z<1) =1-0.8413 =0.1587

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