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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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**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.
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)

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