Question: A shipping company received an order to deliver a load of 1645 packages, transferring them from a warehouse to the showroom for one of its customers. In order to determine which truck to send, the transportation manager needs to determine the approximate weight of the delivery. To do this, he needs to determine the mean weight of the packages.

A. (4) How many randomly selected packages would he need to weigh to estimate, with a 95% confidence, the mean weight within ±1.5 pounds if prior studies indicate that the standard deviation of all weights is around 8 pounds? (Show formula with numbers for credit.)

B. (2) The transportation manager could reduce the required size of the sample EITHER by increasing the amount of error he is willing to accept, OR by:

C. (2) The transportation manager weighs a sample of 120 packages and finds they have a mean weight of 42.1 pounds and a standard deviation of 7.8 pounds. Use the sample data to construct a 95 % confidence interval for the mean package weights.

D. (2) What is the point estimate for the weight of all packages?

What is the margin of error of this weight?

E. (2) Interpret the confidence interval in the context of the original problem.