# Question: An auto manufacturer leases cars to small businesses for use

An auto manufacturer leases cars to small businesses for use in visiting clients and other business travel. The contracted lease does not specify a mileage limit and instead includes a depreciation fee of \$0.30 per mile. The contract includes other origination, maintenance, and damage fees in addition to the fee that covers the mileage. These leases run for one year.
A sample of 150 cars (all were a particular model of four-door sedan) returned to their dealers early in this program averaged 21,714 miles, with standard deviation s = 2,352 miles. Currently, this manufacturer has leased approximately 10,000 of these vehicles. When the program was launched, the planning budget projected that the company would earn (in depreciation fees) \$6,500 on average per car.
Motivation
(a) Should the manufacturer assume that if it were to check every leased car, the average would be 21,714 miles driven?
(b) Can the manufacturer use a confidence interval to check on the claim of \$6,500 earnings in depreciation fees?
Method
(c) Are the conditions for using a 95% confidence interval for the mean number of miles driven per year satisfied?
(d) Does the method of sampling raise any concerns?
(e) Can the manufacturer estimate, with a range, the amount it can expect to earn in depreciation fees per leased vehicle, on average?
Mechanics
(f) Construct the 95% confidence interval for the number of miles driven per year on average for leased cars of this type.
(g) Construct the 95% confidence interval for the earnings over the one-year lease, in a form suitable for presentation. Message
(h) Interpret the 95% confidence interval for the number of miles driven over the one-year period of the lease.
(i) Interpret the 95% confidence interval for the average amount earned per vehicle. What is the implication for the budget claim?
(j) Communicate a range for the total earnings of this program, assuming 10,000 vehicles.

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