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.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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.
Transcribed Image Text: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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