### Understanding Normal Distribution Problem**Problem Statement:**For problem 3, assume the random variable \( x \) is normally distributed with a mean of 86 and a standard deviation of 5. Find the indicated probability.**Problem 3:**\[ \text{P}(x > 89) \]### Explanation:In this problem, we are given a normally distributed random variable \( x \) with a specified mean (μ) and standard deviation (σ). - **Mean (μ)**: 86- **Standard Deviation (σ)**: 5We need to find the probability that \( x \) takes on a value greater than 89, denoted as \( \text{P}(x > 89) \).To solve this, we'll use the properties of the normal distribution:1. **Standardize the Variable**: Convert \( x \) to a standard normal variable \( z \) using the formula:\[ z = \frac{x - \mu}{\sigma} \]2. **Calculate the Z-Score**: For \( x = 89 \),\[ z = \frac{89 - 86}{5} = \frac{3}{5} = 0.6 \]3. **Find the Probability**: Look up the Z-score in the standard normal distribution table (or use a Z-score calculator) to find the probability that \( z \) is less than 0.6. Subtract this value from 1 to find \( \text{P}(z > 0.6) \).Remember, \[ \text{P}(x > 89) = \text{P}(z > 0.6) \]### Conclusion:Using the standard normal distribution table or a calculator will give you the numerical result for the probability \( \text{P}(x > 89) \). This completes the solution approach for the given problem on normal distribution.

To find the indicated probability. P( X > 89) = ?

Answered: For problem 3, assume the random…

For problem 3, assume the random variable x is normally distributed with a mean of 86 and a standard deviation of 5. Find the indicated probability. 3. P(x > 89)

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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