The table to the right shows the number of people testing positive for a certain disease amongst those who do have the disease and amongst those who don't. What percentage of those that don't have the disease tested negative? Round to the nearest tenth of a percent. A. 98.7% OB. 99.8% OC. 86.8% OD. 88.0% Disease No disease Total Test Test positive negative 116 1186 1302 Total 131 15 8683 9869 8698 10,000

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 30E
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The table presented below illustrates the number of people testing positive for a certain disease among those who do have the disease and among those who don't have the disease.

|                 | Test Positive | Test Negative | Total |
|-----------------|---------------|---------------|-------|
| Disease         | 116           | 15            | 131   |
| No disease      | 1186          | 8683          | 9869  |
| Total           | 1302          | 8698          | 10,000|

The table categorizes the testing results into two groups: those with the disease and those without the disease. Each group is further divided into those who tested positive and those who tested negative.

**Question:** What percentage of those who don't have the disease tested negative? Round to the nearest tenth of a percent.

**Answer Options:**
- A. 98.7%
- B. 99.8%
- C. 86.8%
- D. 88.0%

**Explanation:**

To find the percentage of people who do not have the disease but tested negative: 
1. Look at the "No disease" row in the table.
2. The number of people who do not have the disease and tested negative is 8683.
3. The total number of people who do not have the disease is 9869.

Using the formula for percentage:
\[ \text{Percentage} = \left( \frac{\text{number of true negatives}}{\text{total number without disease}} \right) \times 100 \]

\[ \text{Percentage} = \left( \frac{8683}{9869} \right) \times 100 \]

\[ \text{Percentage} \approx 87.9\]

Therefore, the correct answer, rounded to the nearest tenth, is:
- D. 88.0%
Transcribed Image Text:The table presented below illustrates the number of people testing positive for a certain disease among those who do have the disease and among those who don't have the disease. | | Test Positive | Test Negative | Total | |-----------------|---------------|---------------|-------| | Disease | 116 | 15 | 131 | | No disease | 1186 | 8683 | 9869 | | Total | 1302 | 8698 | 10,000| The table categorizes the testing results into two groups: those with the disease and those without the disease. Each group is further divided into those who tested positive and those who tested negative. **Question:** What percentage of those who don't have the disease tested negative? Round to the nearest tenth of a percent. **Answer Options:** - A. 98.7% - B. 99.8% - C. 86.8% - D. 88.0% **Explanation:** To find the percentage of people who do not have the disease but tested negative: 1. Look at the "No disease" row in the table. 2. The number of people who do not have the disease and tested negative is 8683. 3. The total number of people who do not have the disease is 9869. Using the formula for percentage: \[ \text{Percentage} = \left( \frac{\text{number of true negatives}}{\text{total number without disease}} \right) \times 100 \] \[ \text{Percentage} = \left( \frac{8683}{9869} \right) \times 100 \] \[ \text{Percentage} \approx 87.9\] Therefore, the correct answer, rounded to the nearest tenth, is: - D. 88.0%
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