### Probability for a Normally Distributed Random VariableLet \( x \) 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.

The mean and standard deviation are 22 and 5, respectively.

Answered: Let x be a continuous random variable…

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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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