Kat

"An insurance company knows that, in the entire population of millions of insured workers, the mean annual cost of workers’ compensation claims is μ= $439 per insured worker, and the standard deviation is σ= $20,000. The distribution of losses is strongly right-skewed: Most policies have no loss, but a few have large losses, up to millions of dollars.

(a) If the company sells 40,000 policies, what is the shape, mean, and standard

deviation of the sampling distribution of the mean claim loss? Consider these

40,000 policies a random sample of all workers’ compensation insurance

policies.

(b) If the company sells 40,000 policies, what is the probability that the mean

claim loss would be no greater than $500? No greater than $700?"