An insurance company has an automobile policy with a liability limit of $100,000. The probability that the company will incur a loss of at least $50,000 on any one policy is 0.05. Assume the distribution of the loss is well approximated by the normal distribution.

a) What is the expected value of the loss?
b) What is the standard deviation of the loss?
c) What is the probability that the loss on any one policy will be between $25,000 and $75,000?
d) What is the amount that the company should charge for the policy if it wants to make a profit of 20% of the expected value of the loss?

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