Suppose that your wireless mouse has a single battery and that you buy batteries that have a mean lifetime of 6 weeks with a standard deviation of 1.5 weeks. As each battery dies, it is replaced with a new one. Assume that the lifetime of each battery is independent of all others.
(a) Estimate the probability that 14 batteries will last longer than 2 years.
(b) How many batteries should one have on hand in order to be 97.5% condent that new batteries will not need to be purchased within 2 years?