4) 99.7% of the data in a sample was located between the scores 4 and 22. What is the mean and SD for this sample?
4) 99.7% of the data in a sample was located between the scores 4 and 22. What is the mean and SD for this sample?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please solve in a descriptive statistic way
![**Question 4: Statistical Analysis**
99.7% of the data in a sample was located between the scores 4 and 22. What is the mean and standard deviation (SD) for this sample?
**Explanation:**
To find the mean and standard deviation, we can use the empirical rule, which states that approximately 99.7% of the data in a normal distribution lies within three standard deviations (SD) from the mean.
Given:
- 99.7% of data is between scores of 4 and 22.
This implies:
- 4 represents (mean - 3SD)
- 22 represents (mean + 3SD)
Using this information, you can solve for the mean and SD:
1. Calculate the range:
\[
22 - 4 = 18
\]
2. Since this range covers 6 standard deviations (3 on each side of the mean):
\[
6SD = 18
\]
\[
SD = 3
\]
3. Find the mean by calculating the midpoint between 4 and 22:
\[
\text{Mean} = \frac{4 + 22}{2} = 13
\]
Therefore, the mean is 13 and the standard deviation is 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26a21d52-7816-4917-a16a-44de3883c3a3%2Fba0c339e-4641-49ac-8ce7-bd8f076394a6%2Fxg6laj5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 4: Statistical Analysis**
99.7% of the data in a sample was located between the scores 4 and 22. What is the mean and standard deviation (SD) for this sample?
**Explanation:**
To find the mean and standard deviation, we can use the empirical rule, which states that approximately 99.7% of the data in a normal distribution lies within three standard deviations (SD) from the mean.
Given:
- 99.7% of data is between scores of 4 and 22.
This implies:
- 4 represents (mean - 3SD)
- 22 represents (mean + 3SD)
Using this information, you can solve for the mean and SD:
1. Calculate the range:
\[
22 - 4 = 18
\]
2. Since this range covers 6 standard deviations (3 on each side of the mean):
\[
6SD = 18
\]
\[
SD = 3
\]
3. Find the mean by calculating the midpoint between 4 and 22:
\[
\text{Mean} = \frac{4 + 22}{2} = 13
\]
Therefore, the mean is 13 and the standard deviation is 3.
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