The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 264.7 and a standard deviation of 64.4. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 135.9 and 393.5? b. What is the approximate percentage of women with platelet counts between 200.3 and 329.1? C... a. Approximately % of women in this group have platelet counts within 2 standard deviations of the mean, or between 135.9 and 393.5.
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 264.7 and a standard deviation of 64.4. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 135.9 and 393.5? b. What is the approximate percentage of women with platelet counts between 200.3 and 329.1? C... a. Approximately % of women in this group have platelet counts within 2 standard deviations of the mean, or between 135.9 and 393.5.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![**Understanding Blood Platelet Counts using the Empirical Rule**
The blood platelet counts of a group of women exhibit a bell-shaped distribution with a mean of 264.7 and a standard deviation of 64.4. (Note: All units are 1000 cells/μL).
Using the empirical rule, we can calculate the approximate percentages for the following:
**a.** What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 135.9 and 393.5?
**b.** What is the approximate percentage of women with platelet counts between 200.3 and 329.1?
---
**Solving the Questions:**
a. **Approximately** \_\_\_\_\_\_ % of women in this group have platelet counts within 2 standard deviations of the mean, or between 135.9 and 393.5.
(Type an integer or a decimal. Do not round.)
---
**Explanation:**
*The empirical rule* indicates that for a normally distributed dataset:
- Approximately 68% of the data falls within 1 standard deviation of the mean.
- Approximately 95% of the data falls within 2 standard deviations of the mean.
- Approximately 99.7% of the data falls within 3 standard deviations of the mean.
Using this rule, we can determine that approximately 95% of the women will have platelet counts within 2 standard deviations of the mean, which translates to the interval [135.9, 393.5].
**Note:**
The given values are calculated as follows:
- Lower bound: \( 264.7 - 2 \times 64.4 = 135.9 \)
- Upper bound: \( 264.7 + 2 \times 64.4 = 393.5 \)
Readers can utilize this rule to compute similar percentages using the provided mean and standard deviation for normally distributed data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffea94a50-e8e7-419f-bb62-28be718638fb%2Fd79afe67-e3d3-4f2b-a6b9-2d1fb6d90f44%2F3fhk2cs_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Blood Platelet Counts using the Empirical Rule**
The blood platelet counts of a group of women exhibit a bell-shaped distribution with a mean of 264.7 and a standard deviation of 64.4. (Note: All units are 1000 cells/μL).
Using the empirical rule, we can calculate the approximate percentages for the following:
**a.** What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 135.9 and 393.5?
**b.** What is the approximate percentage of women with platelet counts between 200.3 and 329.1?
---
**Solving the Questions:**
a. **Approximately** \_\_\_\_\_\_ % of women in this group have platelet counts within 2 standard deviations of the mean, or between 135.9 and 393.5.
(Type an integer or a decimal. Do not round.)
---
**Explanation:**
*The empirical rule* indicates that for a normally distributed dataset:
- Approximately 68% of the data falls within 1 standard deviation of the mean.
- Approximately 95% of the data falls within 2 standard deviations of the mean.
- Approximately 99.7% of the data falls within 3 standard deviations of the mean.
Using this rule, we can determine that approximately 95% of the women will have platelet counts within 2 standard deviations of the mean, which translates to the interval [135.9, 393.5].
**Note:**
The given values are calculated as follows:
- Lower bound: \( 264.7 - 2 \times 64.4 = 135.9 \)
- Upper bound: \( 264.7 + 2 \times 64.4 = 393.5 \)
Readers can utilize this rule to compute similar percentages using the provided mean and standard deviation for normally distributed data.
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