Question

Problem 9.5. Suppose that an electrical component manufactured by Johnny Depp Electrical

Company is designed to provide a mean service life of 1,000 hours, with a standard deviation of

100 hours. Assume that the service life is normally distributed.

(a) When a customer purchases one component, what is the probability that the service life of the

component will exceed 1,100 hours?

P[ X > 1,100 ] = P[ Z > 1 ] = 15.87%

(b) Suppose that a customer purchases a batch of 64 components, which can be considered a

simple random sample of the population of components. What is the probability that the mean

service life of the 64 components will be less than 1,010 hours?

P[ X-bar < 1,010 ] = P[ Z < 0.8] = 78.81%

(c) Suppose that a customer purchases a batch of 17 components, which can be considered a

simple random sample of the population of components. What is the probability that the sample

variance of the 17 components is more than twice the population variance σ²?

P[s² > 2σ²] = P[ x² > 32] ] ≅ 1.00%

The questions are already answered just need a detailed step by step explanation as to how they derived these answers

Answer 1

This is the solution of part a and give an little bit explanation.

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