In Pawnee, the price of a pound of bacon (X) varies from day to day according to

Question

In Pawnee, the price of a pound of bacon (X) varies from day to day according to normal distribution with mean $4.08 and standard deviation $0.16. The price of a dozen of eggs (Y) also varies from day to day according to normal distribution with mean $1.94 and standard deviation $0.06. Assume the prices of a pound of bacon and a dozen of eggs are independent.

a. Find the probability that on a given day, the price of a pound of bacon is more than twice as expensive as a dozen of eggs. That is, find P(X > 2Y). Give your answer to 4 decimal places.

b. Ron Swanson buys 9 pounds of bacon and 7 dozens of eggs. Find the probability that he paid more than $50. That is, find P (9X + 7Y > 50). Give your answer to 4 decimal places.

Explanation / Answer

a) mean of X-2Y =4.08-2*1.94=0.2

and std deviation of X-2Y =(0.162+(2*0.06)2)1/2 =0.2

hence P(X>2Y) =1-P(X-2Y<0) =1-P(Z<(0-0.2)|/0.2)=1-0.1587=0.8413

b)here mean of 9X+7Y=9*4.08+7*1.94=50.3

and std deviaition=((9*0.16)2+(7*0.06)2)1/2 =1.5

P(9X+7Y>50)=1-P(Z<(50-50.3)/1.5)=1-P(Z<-0.2)=1-0.4207=0.5793

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