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Statistics : Sampling Distributions and Probabilities

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The average annual cost of automobile insurance is $687 (National Association of Insurance Commissioners, January 2003). Use this value as the population mean and assume that the population standard deviation is σ = $230. Consider a sample of 45 automobile insurance policies.

a. Show the sampling distribution of x where x is the sample mean annual cost of automobile insurance.

b. Determine the probability that the sample mean is within $100 of the population mean.

c. Determine the probability that the sample mean is within $25 of the population mean.

d. What would you recommend if an insurance agency wanted the sample mean to estimate the population mean within ± $25?

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Solution Summary

Sampling distributions and probabilities are investigated. The solution is detailed and well presented.

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