Please help with statistics! skewed distributions and probabilities?

[luther]

Based on historical data, an isurance company knows the mean annual cost of workers compensation claims is mu= $439 with a standard deviation of sigma= $20,000. The exact distribution of the claims is unknown, but the company does know the distribution is heavily right-skewed. This is because most of the claims have no cost, but few have a high cost.

QUESTION: Suppose the company sells 40,000 claims. Find the probability the company's average costis less than $500. What figure is the company 99.5% sure the average cost will be less than?

Please help... I think I could solve it if it was normal distribution, but I don't know how to compute with skewed-ness. Calculator solutions work.