The expenditures (in dollars) of customers at a coffee shop has a distribution that is strongly skewed to the right with mean = 3.50 and standard deviation = 2.00.

(a) Suppose 12 customers enter the shop (assume independence). Can you find the probability that the mean expenditure, X , is more than $3.75? If so, find the probability. If not, explain why.

(b) Suppose 100 customers are randomly selected (assume independence). Approxi- mate the probability that the mean expenditure, X , is more than $3.00.

(c) Suppose 100 customers are randomly selected (assume independence). Approxi- mate the probability that the mean expenditure, X , is between than $3.00 and $3.25.

(d) Suppose 100 customers are randomly selected (assume independence). Find the 99th percentile of the sample mean X .

(e) Suppose 400 customers are randomly selected (assume independence). Find the probability that the total expenditure is less than $1,360. Hint: Restate this problem in terms of the sample mean X .