Please answer following answer clearly.
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. What sample size would you recommend if an insurance agency wanted the sample mean to estimate the population mean within $25?
b. What is the probability that the sample mean is within $100 of the population mean?