Given a normal distribution with mean 100 and standard deviation 10, find the number of standard deviations the measurement is from the mean. Express the answer as a positive number. 78 The measurement 78 is standard deviation(s) from the mean. (Type an integer or a decimal.)
Given a normal distribution with mean 100 and standard deviation 10, find the number of standard deviations the measurement is from the mean. Express the answer as a positive number. 78 The measurement 78 is standard deviation(s) from the mean. (Type an integer or a decimal.)
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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Question
![**Problem Statement:**
Given a normal distribution with mean 100 and standard deviation 10, find the number of standard deviations the measurement is from the mean. Express the answer as a positive number.
**Measurement Provided:**
78
---
**Solution Process:**
The measurement 78 is \(\_\_\_\) standard deviation(s) from the mean.
*(Type an integer or a decimal in the answer box)*
---
**Explanation:**
To find how many standard deviations a particular measurement is from the mean, use the formula:
\[
z = \frac{X - \mu}{\sigma}
\]
Where:
- \(X\) is the measurement value
- \(\mu\) is the mean
- \(\sigma\) is the standard deviation
In this case:
- \(X = 78\)
- \(\mu = 100\)
- \(\sigma = 10\)
Calculate \(z\) to express the deviation in terms of standard deviations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f970362-e46d-414b-99ae-39ca4f64716b%2F54fe36a2-b694-456d-80e1-a66d5a4330a1%2Fv2qt4q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given a normal distribution with mean 100 and standard deviation 10, find the number of standard deviations the measurement is from the mean. Express the answer as a positive number.
**Measurement Provided:**
78
---
**Solution Process:**
The measurement 78 is \(\_\_\_\) standard deviation(s) from the mean.
*(Type an integer or a decimal in the answer box)*
---
**Explanation:**
To find how many standard deviations a particular measurement is from the mean, use the formula:
\[
z = \frac{X - \mu}{\sigma}
\]
Where:
- \(X\) is the measurement value
- \(\mu\) is the mean
- \(\sigma\) is the standard deviation
In this case:
- \(X = 78\)
- \(\mu = 100\)
- \(\sigma = 10\)
Calculate \(z\) to express the deviation in terms of standard deviations.
Expert Solution
Step 1
We have given that
Mean(µ) = 100
Standard deviations (σ) = 10
X ~ N (µ, σ)= N(100, 10)
Step by step
Solved in 2 steps
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