Exercise 2 In Pawnee, Indiana, the price of a pound of bacon, X, varies from day

Question

Exercise 2 In Pawnee, Indiana, the price of a pound of bacon, X, varies from day to day according to a normal distribution with mean of $4.12 and a standard deviation of $0.16. The price of a dozen eggs, Y , also varies from day to day according to a normal distribution with a mean of $1.94 and a standard deviation $0.06. Assume the prices of a pound of bacon and a dozen 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 eggs. That is, find P(X > 2Y ). (b) Ron Swanson needs to cook himself breakfast, so he buys 9 pounds of bacon and 7 dozen eggs. Find the probability that he paid more than $50.

Explanation / Answer

a)here expected mean of X-2Y =4.12-2*1.94=0.24

and std deviaiton =(0.162+(2*0.06)2)1/2 =0.2

hence P(X>2Y)=P(X-2Y>0)=P(Z>(0-0.24)/0.2)=P(Z>-1.2)=1-P(Z<-1.2)=1-0.1151 =0.8849

b)

expected value of 9 pound of bacon and 7 dozen eggs =9*4.12+7*1.94=50.66

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

hence probability that he paid more than $50 =P(X>50)=1-P(X<50)=1-P(Z<(50-50.66)/1.5)=1-P(Z<-0.44)

=1-0.3300 =0.6700

Please revert for any explanation required

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