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.

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