Small planes cannot fly well if the payload (people, luggage, and fuel) weighs too much. Suppose that an airline runs a commuter flight that holds 40 people. The airline knows that the weights of passenger plus luggage for typical customers on this flight is approximately normal with a mean of 210 pounds and a standard deviation of 25 pounds.

a. Draw a picture of this distribution.

b. Describe the sampling distribution of the mean weight of passenger plus luggage for a random sample of 40 customers.

c. Draw a picture superimposing the distributions from parts (a) and (b). (Label it clearly, and remember that the total area under each curve must equal 1.)

d. Assume that customers on any particular flight are similar to a random sample. If the total weight of passengers and their luggage should not exceed 8800 pounds, what is the probability that a sold-out flight (40 passengers and their luggage) will exceed the weight limit?

(Hint: Rewrite the desired limit as an average per passenger.)