Cigarette lighters manufactured by EasyVice Company are claimed to have a mean lifetime of 20 months with a standard deviation of 6 months. The money-back guarantee allows you to return the lighter if it does not last at least 12 months from the date of purchase.

a. If the lifetimes of these lighters are normally distributed, what percentage of the lighters will be returned to the company?

b. If a random sample of 25 lighters is tested, what is the probability the sample mean lifetime will be more than 18 months?