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 $4.18 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 Assume the prices of a pound of bacon and a dozen of eggs are deviation $0.06. Assume the prices of a pound of bacon and 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 =4.18-2*1.94=0.3

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<(0-0.3)|/0.2)=P(Z<-1.5)=1-0.0668=0.9332

b)here mean of 9X+7Y=9*4.18+7*1.94=51.2

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

P(9X+7Y>50)=1-P(Z<(50-51.2)/1.5)=1-P(Z<-0.8)=1-0.2119=0.7881

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