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