1. Suppose that yearly health care expenses for a family of four are normally distributed with a mean expense equal to $3,000 and a standard deviation of $500. An insurance company has decided to offer a health insurance premium reduction if a policyholder's health care expenses do not exceed a specified dollar amount. What dollar amount should be established if the insurance company wants families having the lowest 33 percent of yearly health care expenses to be eligible for the premium reduction?
2. Suppose that the 33rd percentile of a normal distribution is equal to 656 and that the 97.5th per- centile of this normal distribution is 896. Find the mean m and the standard deviation s of the normal distribution. Hint: Sketch these percentiles.
CONCEPTS
3. Explain why it might be convenient to approximate binomial probabilities by using areas under an appropriate normal curve.
4. Under what condition may we use the normal approximation to the binomial distribution?
5. Explain how we make a continuity correction. Why is a continuity correction needed when we approximate a binomial distribution by a normal distribution?