According to USA Today, customers are not settling for automobiles straight off the production lines. As an example, those who purchase a $355,000 Rolls-Royce typically add $25,000 in accessories. One of the affordable automobiles to receive additions is BMW’s Mini Cooper. A sample of 179 recent Mini purchasers yielded a sample mean of $5,000 above the $20,200 base sticker price. Suppose the cost of accessories purchased for all Mini Coopers has a standard deviation of $1,500.

a. Calculate a 95% confidence interval for the average cost of accessories on Mini Coopers.

b. Determine the margin of error in estimating the average cost of accessories on Mini Coopers.

c. What sample size would be required to reduce the margin of error by 50%?