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Chapter 4: Problem 39

Suppose you want to find the (approximate) probability that a randomly selected family from Los Angeles earns more than \(\$ 175,000\) a year. How would you find this probability? What procedure would you use? Explain briefly.

Short Answer

Expert verified
Firstly, convert the desired income to a Z-Score by subtracting the mean income from it and dividing by the standard deviation. Then, use a Z-table to find the probability associated with this z-score. Since we want the probability of earning more than \$175,000, subtract the obtained probability from 1. The final result is the approximate probability that a randomly selected family from Los Angeles earns more than \$175,000 a year. Note that to perform this solution, you need the mean and standard deviation of family incomes in Los Angeles.

Step by step solution

01

Understand the data

Before we can solve this problem, it's essential to acknowledge that you need avergae income data of a family in Los Angeles, and the standard deviation of the income. The income will be assumed to follow a normal distribution.
02

Convert to Z-Score

Calculate the difference between the desired income (which is \$175,000 in this case) and the average family income in Los Angeles. Then divide this value by standard deviation of the incomes. This gives the standard deviation units or Z-score, that the desired income lies from the mean income.
03

Look up the Probability in the Z-Table

Once you have the Z-score, you can find the probability associated with any value up to this z-score from the Standard Normal Z-table. This is the probability that a randomly selected family from Los Angeles earns up to \$175,000 a year.
04

Find the required Probability

But we want the probability that a family earns more than \$175,000 a year. To find this, subtract the probability obtained in Step 3 from 1. The resulting value is the desired probability.

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Most popular questions from this chapter

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