Thank you for visiting Part C Use the DCMP Normal Distribution tool at dcmpdatatools utdanacenter org normaldist dcmpdatatools utdanacenter org normaldist to determine the proportion of healthy adults you. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To solve this problem, we are going to use the concept of normal distribution. A normal distribution is a bell-shaped distribution that is symmetric about the mean. We'll use the mean and standard deviation to find the necessary values.
### Part C: Proportion of healthy adults with body temperatures below 97.8 degrees
1. Understand the Parameters:
- We are assuming the average body temperature (mean) of healthy adults is 98.6 degrees Fahrenheit.
- The standard deviation for body temperature is assumed to be 0.7 degrees.
2. Find the Z-score:
- The Z-score is a measure of how many standard deviations a data point is from the mean. The formula for the Z-score is:
[tex]\[
Z = \frac{(X - \text{mean})}{\text{standard deviation}}
\][/tex]
- Here, [tex]\( X \)[/tex] is 97.8 degrees.
- So, calculate the Z-score:
[tex]\[
Z = \frac{(97.8 - 98.6)}{0.7} = -1.14
\][/tex]
3. Find the Proportion:
- Use the Z-score to find the cumulative probability from the standard normal distribution table (or tool). This gives us the proportion of the population with a body temperature below 97.8 degrees.
- The result for this is approximately 0.13, meaning 13% of the population.
### Part D: Body temperature for the top 1% of healthy adults
1. Find the Z-score for the Top 1%:
- We want to find the body temperature at which only 1% of the population is above it. This refers to the 99th percentile.
- The Z-score corresponding to the 99th percentile is approximately 2.33.
2. Calculate the required body temperature:
- Use the Z-score to find the X value (body temperature) using the formula:
[tex]\[
X = \text{mean} + (Z \times \text{standard deviation})
\][/tex]
- Substitute the values:
[tex]\[
X = 98.6 + (2.33 \times 0.7) = 100.23
\][/tex]
3. Result:
- Therefore, the top 1% of healthy adults would have a body temperature of at least 100.23 degrees Fahrenheit.
In conclusion, 13% of healthy adults have body temperatures below 97.8 degrees, and the body temperature at least 100.23 degrees would place someone in the top 1% of healthy adults.
### Part C: Proportion of healthy adults with body temperatures below 97.8 degrees
1. Understand the Parameters:
- We are assuming the average body temperature (mean) of healthy adults is 98.6 degrees Fahrenheit.
- The standard deviation for body temperature is assumed to be 0.7 degrees.
2. Find the Z-score:
- The Z-score is a measure of how many standard deviations a data point is from the mean. The formula for the Z-score is:
[tex]\[
Z = \frac{(X - \text{mean})}{\text{standard deviation}}
\][/tex]
- Here, [tex]\( X \)[/tex] is 97.8 degrees.
- So, calculate the Z-score:
[tex]\[
Z = \frac{(97.8 - 98.6)}{0.7} = -1.14
\][/tex]
3. Find the Proportion:
- Use the Z-score to find the cumulative probability from the standard normal distribution table (or tool). This gives us the proportion of the population with a body temperature below 97.8 degrees.
- The result for this is approximately 0.13, meaning 13% of the population.
### Part D: Body temperature for the top 1% of healthy adults
1. Find the Z-score for the Top 1%:
- We want to find the body temperature at which only 1% of the population is above it. This refers to the 99th percentile.
- The Z-score corresponding to the 99th percentile is approximately 2.33.
2. Calculate the required body temperature:
- Use the Z-score to find the X value (body temperature) using the formula:
[tex]\[
X = \text{mean} + (Z \times \text{standard deviation})
\][/tex]
- Substitute the values:
[tex]\[
X = 98.6 + (2.33 \times 0.7) = 100.23
\][/tex]
3. Result:
- Therefore, the top 1% of healthy adults would have a body temperature of at least 100.23 degrees Fahrenheit.
In conclusion, 13% of healthy adults have body temperatures below 97.8 degrees, and the body temperature at least 100.23 degrees would place someone in the top 1% of healthy adults.
Thank you for reading the article Part C Use the DCMP Normal Distribution tool at dcmpdatatools utdanacenter org normaldist dcmpdatatools utdanacenter org normaldist to determine the proportion of healthy adults you. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
