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? 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.)
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? 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.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
I need help with this one please thank you!
![## Empirical Rule and Blood Platelet Counts
### Context
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.)
### Questions
**a. What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean (between 135.9 and 393.5)?**
**b. What is the approximate percentage of women with platelet counts between 200.3 and 329.1?**
### Detailed Solution
**a.** The empirical rule (also known as the 68-95-99.7 rule) states that for a normal distribution:
- 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.
Given that the mean is 264.7 and the standard deviation is 64.4, we calculate:
- \[ Mean - 2 \times \text{Standard Deviation} = 264.7 - 2 \times 64.4 = 135.9 \]
- \[ Mean + 2 \times \text{Standard Deviation} = 264.7 + 2 \times 64.4 = 393.5 \]
Hence, approximately **95%** of women in this group have platelet counts within this range.
---
In summary, the empirical rule helps to understand the distribution of data in a bell-shaped (normal) curve. In this case, approximately 95% of the women have blood platelet counts between 135.9 and 393.5 (thousand cells/μL).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffea94a50-e8e7-419f-bb62-28be718638fb%2F5b694c23-af2f-4829-b514-2df98c32166d%2F21n8hz_processed.png&w=3840&q=75)
Transcribed Image Text:## Empirical Rule and Blood Platelet Counts
### Context
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.)
### Questions
**a. What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean (between 135.9 and 393.5)?**
**b. What is the approximate percentage of women with platelet counts between 200.3 and 329.1?**
### Detailed Solution
**a.** The empirical rule (also known as the 68-95-99.7 rule) states that for a normal distribution:
- 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.
Given that the mean is 264.7 and the standard deviation is 64.4, we calculate:
- \[ Mean - 2 \times \text{Standard Deviation} = 264.7 - 2 \times 64.4 = 135.9 \]
- \[ Mean + 2 \times \text{Standard Deviation} = 264.7 + 2 \times 64.4 = 393.5 \]
Hence, approximately **95%** of women in this group have platelet counts within this range.
---
In summary, the empirical rule helps to understand the distribution of data in a bell-shaped (normal) curve. In this case, approximately 95% of the women have blood platelet counts between 135.9 and 393.5 (thousand cells/μL).
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
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman