As part of determining what to charge for its policies, an insurance company (SAADA Insurance) needs to estimate the average cost of bodily injury claims paid out when the company’s policyholder is at fault, based on a random sample of past claims. They’d like to be 95% confident that the estimate is within ± $200, and their best guess is that the standard deviation for bodily injury claims is around $8,000. What sample size should be used?

SAADA Insurance would also like to estimate the proportion of times that an accident caused by one of their policyholders results in a bodily injury claim. They know that, for their industry, this proportion is equal to 22%, so it seems reasonable to assume that this value might also apply to SAADA Insurance. (It’s a good initial guess.) Once again, the estimate will be based on looking at a random sample of past claims. What sample size should be used if SAADA wishes to estimate this proportion to within ±0.05 with 98% confidence?