# Suppose that yearly health care expenses for a family of four are normally distributed with a...

## Question:

Suppose that yearly health care expenses for a family of four are normally distributed with a mean expense equal to $4,801 and a standard deviation of $402. An insurance company has decided of 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?

## Normal Distribution and Percentiles

When looking for a percentile under the normal distribution for a given {eq}\mu {/eq} and {eq}\sigma {/eq}, use the standard normal distribution as a starting point. Locate the z-score associated with the given area and then apply the z-score formula to answer the question.

## Answer and Explanation:

When answering this question, we'll follow these steps.

**1.** Let's define {eq}X
{/eq} as health care expenses. Then, {eq}X\sim...

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#### Learn more about this topic:

from Introduction to Psychology: Homework Help Resource

Chapter 13 / Lesson 7