MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Transcription:**
Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.
If \( P(-b < z < b) = 0.9008 \), find \( b \).
\( b = \) [ ]
**Explanation:**
This problem involves finding the value of \( b \) such that the probability that a standard normal variable \( z \) falls between \(-b\) and \(b\) is 0.9008. The standard normal distribution follows a bell curve, centered at 0 with a spread determined by the standard deviation (in this case, 1).
The goal is to determine the z-scores on the standard normal distribution curve that correspond to a cumulative probability of 0.9008. This involves understanding the concept of z-scores and using the standard normal distribution table or technology to find the appropriate values of \( b \).](https://content.bartleby.com/qna-images/question/e9d8e919-6c53-43b3-96c1-5f9438fdaf13/ac0343f5-9ffc-41a0-9ae3-696ba3ba89dd/i48c8c5_processed.jpeg)
Transcribed Image Text:**Transcription:**
Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.
If \( P(-b < z < b) = 0.9008 \), find \( b \).
\( b = \) [ ]
**Explanation:**
This problem involves finding the value of \( b \) such that the probability that a standard normal variable \( z \) falls between \(-b\) and \(b\) is 0.9008. The standard normal distribution follows a bell curve, centered at 0 with a spread determined by the standard deviation (in this case, 1).
The goal is to determine the z-scores on the standard normal distribution curve that correspond to a cumulative probability of 0.9008. This involves understanding the concept of z-scores and using the standard normal distribution table or technology to find the appropriate values of \( b \).
Expert Solution
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Step 1
The question is about std. normal distribution
Given :
z N ( 0, 1 )
P ( -b < z < b ) = 0.9008
To find :
Value of b
Step by stepSolved in 2 steps with 2 images
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