According to her doctor, Mrs. Cooper's cholesterol level is higher than only 15% of the females aged 50 and over. The cholesterol levels among females aged 50 mg mg and over are approximately normally distributed with a mean of 240 and a standard deviation of 25 . What is Mrs. Cooper's cholesterol level? Carry dL dL your intermediate computations to at least four decimal places. Round your answer to one decimal place. 0 ? mg dL
According to her doctor, Mrs. Cooper's cholesterol level is higher than only 15% of the females aged 50 and over. The cholesterol levels among females aged 50 mg mg and over are approximately normally distributed with a mean of 240 and a standard deviation of 25 . What is Mrs. Cooper's cholesterol level? Carry dL dL your intermediate computations to at least four decimal places. Round your answer to one decimal place. 0 ? mg dL
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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![### Educational Content Transcription
---
**Problem Description:**
According to her doctor, Mrs. Cooper's cholesterol level is higher than only 15% of the females aged 50 and over. The cholesterol levels among females aged 50 and over are approximately normally distributed with a mean of 240 mg/dL and a standard deviation of 25 mg/dL.
**Question:**
What is Mrs. Cooper’s cholesterol level? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.
---
**Explanation Area:**
- **Given Data:**
- Mean (μ): 240 mg/dL
- Standard Deviation (σ): 25 mg/dL
- Percentile: 85% (since cholesterol level higher than only 15% means Mrs. Cooper belongs to the 85th percentile)
- **Relevant Formula:**
To find Mrs. Cooper's cholesterol level, we need to use the z-score formula:
\[
Z = \frac{X - \mu}{\sigma}
\]
Where \( Z \) is the z-score, \( X \) is the cholesterol level, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
- **Steps to Find Cholesterol Level:**
1. Find the z-score corresponding to the 85th percentile.
2. Use the z-score formula to calculate the cholesterol level \( X \).
**Computation Area:**
1. **Finding z-score:**
- For the 85th percentile, refer to the z-table or use a standard normal distribution calculator.
- \( Z \approx 1.0364 \) for the 85th percentile.
2. **Calculating Cholesterol Level:**
- Rearrange the z-score formula to solve for \( X \):
\[
X = Z \cdot \sigma + \mu
\]
- Substitute the values:
\[
X = (1.0364 \cdot 25) + 240
\]
- Perform the calculation:
\[
X \approx 25.91 + 240 \approx 265.9
\]
**Final Answer:**
Mrs. Cooper’s cholesterol level is approximately \( 265.9 \) mg/dL.
---
**Interaction Options:**
- **Explanation**: Offers](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd1b6d45-a7eb-422c-8cfa-b963b51ff783%2Feb58deec-2c99-4698-9308-1fc097ad6269%2Ffwojxhu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Content Transcription
---
**Problem Description:**
According to her doctor, Mrs. Cooper's cholesterol level is higher than only 15% of the females aged 50 and over. The cholesterol levels among females aged 50 and over are approximately normally distributed with a mean of 240 mg/dL and a standard deviation of 25 mg/dL.
**Question:**
What is Mrs. Cooper’s cholesterol level? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.
---
**Explanation Area:**
- **Given Data:**
- Mean (μ): 240 mg/dL
- Standard Deviation (σ): 25 mg/dL
- Percentile: 85% (since cholesterol level higher than only 15% means Mrs. Cooper belongs to the 85th percentile)
- **Relevant Formula:**
To find Mrs. Cooper's cholesterol level, we need to use the z-score formula:
\[
Z = \frac{X - \mu}{\sigma}
\]
Where \( Z \) is the z-score, \( X \) is the cholesterol level, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
- **Steps to Find Cholesterol Level:**
1. Find the z-score corresponding to the 85th percentile.
2. Use the z-score formula to calculate the cholesterol level \( X \).
**Computation Area:**
1. **Finding z-score:**
- For the 85th percentile, refer to the z-table or use a standard normal distribution calculator.
- \( Z \approx 1.0364 \) for the 85th percentile.
2. **Calculating Cholesterol Level:**
- Rearrange the z-score formula to solve for \( X \):
\[
X = Z \cdot \sigma + \mu
\]
- Substitute the values:
\[
X = (1.0364 \cdot 25) + 240
\]
- Perform the calculation:
\[
X \approx 25.91 + 240 \approx 265.9
\]
**Final Answer:**
Mrs. Cooper’s cholesterol level is approximately \( 265.9 \) mg/dL.
---
**Interaction Options:**
- **Explanation**: Offers
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