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Assume that the random variable X is normally distributed, with mean = 62 and standard deviation a= 10. Compute the probability P(55

Assume that the random variable X is normally distributed, with mean = 62 and standard deviation a= 10. Compute the probability P(55

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
Problem 1P
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### Problem Statement Assume that the random variable \( X \) is normally distributed, with a mean \( \mu = 62 \) and standard deviation \( \sigma = 10 \). Compute the probability \( P(55 < X < 70) \). Be sure to draw a normal curve with the area corresponding to the probability shaded. ### Resources - [Click here to view the standard normal distribution table (page 1).](#) - [Click here to view the standard normal distribution table (page 2).](#) ### Question Draw a normal curve with the area corresponding to the probability shaded. Choose the correct graph below: - **Option A**: Graph showing a normal distribution with the area between \( X = 55 \) and \( X = 70 \) shaded, centered around the mean. - **Option B**: Graph showing a normal distribution, shaded area extending slightly beyond \( X = 70 \). - **Option C**: Graph showing an incorrect range with the area shaded symmetrically around the mean. - **Option D**: Graph showing a normal distribution with the area between \( X = 55 \) and \( X = 70 \), but with less shading than option A. When interpreting each graph, ensure to check if the shaded part accurately represents the probability \( P(55 < X < 70) \).
Transcribed Image Text:### Problem Statement Assume that the random variable \( X \) is normally distributed, with a mean \( \mu = 62 \) and standard deviation \( \sigma = 10 \). Compute the probability \( P(55 < X < 70) \). Be sure to draw a normal curve with the area corresponding to the probability shaded. ### Resources - [Click here to view the standard normal distribution table (page 1).](#) - [Click here to view the standard normal distribution table (page 2).](#) ### Question Draw a normal curve with the area corresponding to the probability shaded. Choose the correct graph below: - **Option A**: Graph showing a normal distribution with the area between \( X = 55 \) and \( X = 70 \) shaded, centered around the mean. - **Option B**: Graph showing a normal distribution, shaded area extending slightly beyond \( X = 70 \). - **Option C**: Graph showing an incorrect range with the area shaded symmetrically around the mean. - **Option D**: Graph showing a normal distribution with the area between \( X = 55 \) and \( X = 70 \), but with less shading than option A. When interpreting each graph, ensure to check if the shaded part accurately represents the probability \( P(55 < X < 70) \).
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