Suppose that yearly health care expenses for a family of four are normally distr

Question

Suppose that yearly health care expenses for a family of four are normally distributed with a mean expense equal to $4,906 and a standard deviation of $786. 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? (Round answer to nearest whole dollar amount.)

Explanation / Answer

Let X denote the yearly health care expenses for a family of four, then X follows normal distribution with µ=$4,906 and =$786

Let x0 be the dollar amount that 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.

Then P(X<x0)=0.33

Using excel function =norminv(0.33,4906,786), we get x0= 4560.228$4560

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.