At a certain coffee shop, all the customers buy a cup of coffee and some also bu

Question

At a certain coffee shop, all the customers buy a cup of coffee and some also buy a donut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 310 cups and a standard deviation of 25 cups. He also believes that the number of donuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 130 donuts and a standard deviation of 12. -The shop is open every day but Sunday. Assuming day-to-day sales are independent, what's the probability he'll sell a donut to more than half his coffee customers?

Explanation / Answer

Solution:- = 130 - 1/2(310)
= 130 - 155
= -25
Var(Y) = Var(D) + Var(0.5C)
= 12^2+0.25*25^2 =300.25
= sqrt(300.25) = 17.33

Z = (0 + 25)/17.33 = 1.4425
P( Z>1.4425 )= 1P( Z<1.4425 )
= 10.9251
= 0.0749

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