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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
Related questions
Question
I need help with this one please thank you
![**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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 4 images
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt