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 $3,711 and a standard deviation of $103. 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.)

Suppose that yearly health care expenses for a family of four are normally distributed with a mean expense equal to $3,711 and a standard deviation of $103. 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

mean expense is equal to $3,711 and a standard deviation is $103

we need to find the z value that corresponds to 0.33 , if we find the z for 1-0.33 i.e for 0.67, we need to negate it . thus from normal distribution table we get -0.44

thus answer is mean+s*z =3711-0.44*103=3665.68 or 3666

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