Question Help Assume that human body temperatures are normally distributed with a mean of 98.23°F and a standard deviation of 0.61°F a. A hospital uses 100.6°F as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6°F is appropriate? b. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 5.0% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive, but the subject is not really sick.) Click to view page 1 of the table. Click to view page 2 of the table

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### Understanding Human Body Temperatures

Human body temperatures are typically normally distributed with a mean of 98.23°F and a standard deviation of 0.61°F. This information can be used to analyze and determine various aspects such as what constitutes a fever or setting medical thresholds.

#### Scenario Analysis:
1. **Hospital Fever Threshold:**
   - Suppose a hospital uses 100.6°F as the lowest temperature considered to be a fever.
   - Question: What percentage of normal and healthy persons would have a body temperature considered to be a fever with this threshold?
   - Consideration: Does this percentage suggest that the 100.6°F cutoff is appropriate?

2. **Setting Medical Thresholds:**
   - Physicians aim to identify a minimum temperature for further medical tests.
   - The goal is to determine this threshold so that only 5.0% of healthy people would be considered to have a fever (leading to a false positive, where the individual is not actually sick).
   - Question: What should the minimum temperature be to ensure this 5.0% false positive rate?

#### Calculation Tasks:
- **Part A:** Determine the percentage of healthy individuals considered to have a fever at the 100.6°F threshold.
  - Input required: The answer rounded to two decimal places as needed.
  
  ```Answer Box: [Percentage of healthy persons] %```

- **Part B:** Determine the new minimum temperature threshold that would result in only 5.0% of healthy individuals exceeding it.

  ```Answer Box: [New temperature threshold] °F```

---

You are provided with options to view additional pages for tables, which may contain statistical data or values from the standard normal distribution (Z-table) needed to complete these calculations.

#### Navigation Instructions:
- Click on the links to view essential tables:
  - [Page 1 of the table]
  - [Page 2 of the table]

Make sure to correctly enter your answer in the answer box and click "Check Answer" to validate your input. Partial progress is indicated at the bottom of the page.

---

### Educational Insights:
This analysis can help students understand the applications of normal distribution in real-world scenarios, especially in medical settings. It illustrates how statistical thresholds are set and the implications of false positives in diagnosing conditions based on body temperature.
Transcribed Image Text:### Understanding Human Body Temperatures Human body temperatures are typically normally distributed with a mean of 98.23°F and a standard deviation of 0.61°F. This information can be used to analyze and determine various aspects such as what constitutes a fever or setting medical thresholds. #### Scenario Analysis: 1. **Hospital Fever Threshold:** - Suppose a hospital uses 100.6°F as the lowest temperature considered to be a fever. - Question: What percentage of normal and healthy persons would have a body temperature considered to be a fever with this threshold? - Consideration: Does this percentage suggest that the 100.6°F cutoff is appropriate? 2. **Setting Medical Thresholds:** - Physicians aim to identify a minimum temperature for further medical tests. - The goal is to determine this threshold so that only 5.0% of healthy people would be considered to have a fever (leading to a false positive, where the individual is not actually sick). - Question: What should the minimum temperature be to ensure this 5.0% false positive rate? #### Calculation Tasks: - **Part A:** Determine the percentage of healthy individuals considered to have a fever at the 100.6°F threshold. - Input required: The answer rounded to two decimal places as needed. ```Answer Box: [Percentage of healthy persons] %``` - **Part B:** Determine the new minimum temperature threshold that would result in only 5.0% of healthy individuals exceeding it. ```Answer Box: [New temperature threshold] °F``` --- You are provided with options to view additional pages for tables, which may contain statistical data or values from the standard normal distribution (Z-table) needed to complete these calculations. #### Navigation Instructions: - Click on the links to view essential tables: - [Page 1 of the table] - [Page 2 of the table] Make sure to correctly enter your answer in the answer box and click "Check Answer" to validate your input. Partial progress is indicated at the bottom of the page. --- ### Educational Insights: This analysis can help students understand the applications of normal distribution in real-world scenarios, especially in medical settings. It illustrates how statistical thresholds are set and the implications of false positives in diagnosing conditions based on body temperature.
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