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Let x be a continuous random variable that is normally distributed with a mean of 22 and a standard deviation of 5. Find to 4 d places the probability that x assumes a value a. between 26 and 34. Probability = i b. between 18 and 31. Probability = i

Let x be a continuous random variable that is normally distributed with a mean of 22 and a standard deviation of 5. Find to 4 d places the probability that x assumes a value a. between 26 and 34. Probability = i b. between 18 and 31. Probability = i

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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### Probability for a Normally Distributed Random Variable Let \( x \) be a continuous random variable that is normally distributed with a mean \( \mu \) of 22 and a standard deviation \( \sigma \) of 5. Below are the calculations for the probabilities that \( x \) assumes a value within specified ranges. #### a. Probability that \( x \) is between 26 and 34 \[ \text{Probability} = \boxed{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \] #### b. Probability that \( x \) is between 18 and 31 \[ \text{Probability} = \boxed{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \] These probabilities can be found by standardizing the normal distribution and using the cumulative distribution function (CDF) of the standard normal distribution. Each boxed area represents an input field where the calculated probability to 4 decimal places will be entered.
Transcribed Image Text:### Probability for a Normally Distributed Random Variable Let \( x \) be a continuous random variable that is normally distributed with a mean \( \mu \) of 22 and a standard deviation \( \sigma \) of 5. Below are the calculations for the probabilities that \( x \) assumes a value within specified ranges. #### a. Probability that \( x \) is between 26 and 34 \[ \text{Probability} = \boxed{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \] #### b. Probability that \( x \) is between 18 and 31 \[ \text{Probability} = \boxed{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \] These probabilities can be found by standardizing the normal distribution and using the cumulative distribution function (CDF) of the standard normal distribution. Each boxed area represents an input field where the calculated probability to 4 decimal places will be entered.
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