6. Suppose that a brand of AA batteries reaches a significant milestone to their death on

average after 7.36 hours, with standard deviation of 0.29 hours. Assume that when

this milestone occurs follows a normal distribution

(a) Calculate the probability that a battery does not reach this milestone in its first

8 hours of usage.

(b) Suppose that the company wants to sell a pack of n batteries of which (at least)

10 will last until after 7.5 hours of usage. If n = 12, what is the probability of

this goal being met?

(c) How many batteries n should be in the package in order for the probability to

exceed 1%? Give the smallest number n which works.