Question

The management at JLP Airlines uses a normal distribution to model the weight of luggage checked in by passengers flying between New York and Dallas. The mean weight of luggage checked by an economy class passenger is 40 pounds with a standard deviation of 10 pounds. The mean weight for a first-class passenger is 30 pounds, with a standard deviation of 6 pounds.

(a) What is the probability that an economy class passenger checks between 32 and 36 pounds of luggage?

(b) Suppose a random sample of sixteen first class passengers are selected. What is the mean weight of luggage above which only 2.5% of all first-class passengers check in?

(c) The airline claims, based on its historical records, that the proportion of economy class passengers who check in more than 35 pounds is more than 60 percent. If a sample of 36 economy class passengers is selected at random and eighteen checked in more than 35 pounds in luggage weight, what is the probability that the airline’s claim is true?

(d) Suppose we sample 50 economy class passengers and 20 first class passengers. What is the probability that economy class passengers check in a mean luggage weight of more than that of first-class passengers?

(e) Go back to part(b). You used a sample size of 16 first class passengers to answer the question. Now, what sample size would you select if you wanted to estimate the mean luggage weight of first-class passengers with the bound on the error of estimation to be no more than 1.5 pounds? Use a level of significance of 10% (alpha = 0.10).

Answer 1