Consider a particular genetic disease affects % of adults in the U.S. population (for the value of x to use, see below). Fortunately, there is a genetic test for the gene that causes the disease. The test is 98% accurate; that is, 98% of the people who take the test get the correct result (and 2% of people tested get the wrong result). In Smithville, there are 200,000 adults, and they all get tested for the disease. mi 1. How many of the residents of Smithville are likely to have the disease? 2. How many of the people who actually have the disease get a positive test result? 3. How many of the people who do not have the disease get a positive test result? 4. Of the people who get a positive test result, how many of them have the disease? Convert this to a percentage: What percent of people who get a positive result actually have the disease? 5. What does this percentage tell you about the test?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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100%

(X=2 )

### Understanding Genetic Disease Testing Accuracy

Consider a particular genetic disease affects \( x\% \) of adults in the U.S. population. For the value of \( x \) to use, see the instructions below. Fortunately, there is a genetic test for the gene that causes the disease. The test is 98% accurate; that is, 98% of the people who take the test get the correct result (and 2% of people tested get the wrong result).

In Smithville, there are 200,000 adults, all of whom get tested for the disease.

#### Questions for Analysis:

1. **How many of the residents of Smithville are likely to have the disease?**
2. **How many of the people who actually have the disease get a positive test result?**
3. **How many of the people who do not have the disease get a positive test result?**
4. **Of the people who get a positive test result, how many of them have the disease? Convert this to a percentage: What percent of people who get a positive result actually have the disease?**
5. **What does this percentage tell you about the test?**

#### Explanation of Diagram:
To the right of the text, there is an image of a DNA double helix structure. This image symbolizes the genetic underpinnings of the disease being tested and provides a visual representation of the focus on genetic markers and testing accuracy.

This set of questions aims to guide students through the process of understanding and interpreting the statistical accuracy of genetic testing within a population, reinforcing key concepts in genetics and probability.
Transcribed Image Text:### Understanding Genetic Disease Testing Accuracy Consider a particular genetic disease affects \( x\% \) of adults in the U.S. population. For the value of \( x \) to use, see the instructions below. Fortunately, there is a genetic test for the gene that causes the disease. The test is 98% accurate; that is, 98% of the people who take the test get the correct result (and 2% of people tested get the wrong result). In Smithville, there are 200,000 adults, all of whom get tested for the disease. #### Questions for Analysis: 1. **How many of the residents of Smithville are likely to have the disease?** 2. **How many of the people who actually have the disease get a positive test result?** 3. **How many of the people who do not have the disease get a positive test result?** 4. **Of the people who get a positive test result, how many of them have the disease? Convert this to a percentage: What percent of people who get a positive result actually have the disease?** 5. **What does this percentage tell you about the test?** #### Explanation of Diagram: To the right of the text, there is an image of a DNA double helix structure. This image symbolizes the genetic underpinnings of the disease being tested and provides a visual representation of the focus on genetic markers and testing accuracy. This set of questions aims to guide students through the process of understanding and interpreting the statistical accuracy of genetic testing within a population, reinforcing key concepts in genetics and probability.
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