### Probability Calculation for Normally Distributed Random VariablesLet \( x \) be a continuous random variable that is normally distributed with a mean of 56 and a standard deviation of 14. Find to 4 decimal places the probability that \( x \) assumes a value:1. **Less than 38** - Probability: [Insert answer here]2. **Greater than 72** - Probability: [Insert answer here]3. **Greater than 38** - Probability: [Insert answer here]4. **Less than 63** - Probability: [Insert answer here]#### Explanation:To solve these problems, you can use the standard normal distribution (z-score) formula:\[ Z = \frac{X - \mu}{\sigma} \]Where:- \( X \) is the value from the distribution- \( \mu \) is the mean of the distribution- \( \sigma \) is the standard deviation of the distribution- \( Z \) is the z-score corresponding to the value \( X \)Once the z-score is calculated, you can use standard normal distribution tables or software/calculators to find the corresponding probabilities.For each given condition (less than 38, greater than 72, etc.), calculate the z-score and then determine the cumulative probability from the Z-table or appropriate function in a statistical software/calculator.

The mean and standard deviation are 56 and 14, 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 56 and a standard deviation of 14 places the probability that x assumes a value a. less than 38 i b. greater than 72 i c. greater than 38 d. less than 63