show all steps In Anytown, the price of a gallon of milk (X) varies from day to

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In Anytown, the price of a gallon of milk (X) varies from day to day according to normal distribution with mean $2.8 and standard deviation $0.20. The price of a package of Oreo cookies (Y) also varies from day to day according to normal distribution with mean $2.6 and standard deviation $0.15. Assume the prices of a gallon of milk and a package of Oreo cookies are independent. a. Find the probability that on a given day, the price of a package of Oreo cookies is higher than the price of a gallon of milk. That is, find P (Y > X). Give your answer to 4 decimal places. b. Alex is planning a Milk-and-Oreos party for his imaginary friends. He buys 4 gallons of milk and 7 packages of Oreo cookies. Find the probability that he paid less than $30. That is, find P(4X + 7Y

Explanation / Answer

a) here mean of X-Y =2.8-2.6=0.2

and std deviation of X-Y =(0.22+0.152)1/2 =0.25

hence P(X-Y<0) =P(Z<(0-0.2)/0.25)=P(Z<-0.8)= 0.2118

b) mean of 4x+7y =4*2.8+7*2.6=29.4

and std deviation =(16*0.22+49*0.152)1/2 =1.0332

hence P(4X+7Y<30)=P(Z<(30-29.4)/1.0332)=P(Z<0.5807)=0.7193

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