An economist uses the price of a gallon of milk as a measure of inflation. She f

Question

An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.50 per gallon and the population standard deviation is $0.33. You decide to sample 40 convenience stores, collect their prices for a gallon of milk, and com-pute the mean price for the sample.a. What is the standard error of the mean in this experiment?b. What is the probability that the sample mean is between $3.46 and $3.54?c. What is the probability that the difference between the sample mean and the population mean is less than $0.01?d. What is the likelihood the sample mean is greater than $3.60?

Explanation / Answer

standard error of the mean =std deviation/(n)1/2 =0.0522

b)P(3.46<X<3..54) =P((3.46-3.50)/0.0522<Z<(3.54-3.50)/0.0522)=P(-0.7666<Z<0.7666)=0.7783-0.2217=0.5567

c)P(-0.01/0.0.522<Z<(0.01/0.0522)=P(-0.1917<Z<0.1917)=0.5760-0.4240=0.1520

d)P(X>3.60)=1-P(Z<1.9165)=1-0.9724=0.0276

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