Car buyers often add accessories to their new cars. A sample of 179 Mini Cooper purchasers yielded a sample mean of $5,000 worth of accessories added to the purchase above the $20,200 base sticker price.

Suppose the cost of accessories purchased for all Minis has a standard deviation of $1,500.

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

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

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