Hi, I'm having troubles solving this stardard normal distribution if anyone can help! Steps would really help me understand as well!
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?
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?
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The z value that marks the lower 33% of the standard normal distribution is -0.4399, since
p(x ≤ -0.4399) = 0.33
We also know that
z = (x - µ)/σ
so we have
-0.4399 = (x - 3000)/500
x = 3000 + 500(-0.4399) = 3000 - 219.95
x = $2780.05
p(x ≤ -0.4399) = 0.33
We also know that
z = (x - µ)/σ
so we have
-0.4399 = (x - 3000)/500
x = 3000 + 500(-0.4399) = 3000 - 219.95
x = $2780.05