An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is μ = $250 and the standard deviation of the loss is σ = $5000. The distribution of losses is strongly right-skewed: many policies have $0 loss, but a few have large losses. The company hopes to sell 1000 of these policies for $300 each.

a. Assuming that the company’s claim is true, what is the probability that the mean loss from fire is greater than $300 for an SRS of 1000 homeowners?

b. If the company wants to be 90% certain that the mean loss from fire in an SRS of 1000 homeowners is less than the amount it charges for the policy, how much should the company charge?