Q: Assume that the random variable Z follows a standard normal distribution. Select the appropriate answer for the following graph. ### Understanding the Standard Normal Distribution#### Graph ExplanationThe image shows a bell-shaped curve representing the standard normal distribution, which is symmetrical about the vertical axis (z = 0). - **Shaded Area**: The area shaded in gray on the graph indicates the probability of the standard normal variable, Z, falling within a specific range.- **Axes**: - The horizontal axis (z-axis) is labeled with standard deviations ranging from -3 to 3. - The vertical line at z = 0 is the mean of the distribution.#### Multiple Choice OptionsThe graph is used to evaluate the probabilities associated with the z-values for a standard normal distribution. The options provided are:1. ○ P(Z < -1.5)2. ○ P(-2.00 < Z < 2.00)3. ○ P(Z > 1.5)4. ○ P(Z < 1.96)5. ○ P₈₅6. ● P₂₅The correct choice likely relates to the shaded region; however, interpretation requires specific information about the shading, which appears broader than a specific z-value like those mentioned in the options.#### Concept ReviewThe standard normal distribution is a key concept in statistics used to measure probabilities and understand data patterns relative to the mean and standard deviation. Understanding how to read and interpret this distribution is fundamental to analyzing statistical data.

Here use normal distribution table for probability from z score

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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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Q: Assume that the random variable Z follows a standard normal distribution. Select the appropriate answer for the following graph.

### Understanding the Standard Normal Distribution

#### Graph Explanation

The image shows a bell-shaped curve representing the standard normal distribution, which is symmetrical about the vertical axis (z = 0).

- **Shaded Area**: The area shaded in gray on the graph indicates the probability of the standard normal variable, Z, falling within a specific range.
- **Axes**:
- The horizontal axis (z-axis) is labeled with standard deviations ranging from -3 to 3.
- The vertical line at z = 0 is the mean of the distribution.

#### Multiple Choice Options

The graph is used to evaluate the probabilities associated with the z-values for a standard normal distribution. The options provided are:

1. ○ P(Z < -1.5)
2. ○ P(-2.00 < Z < 2.00)
3. ○ P(Z > 1.5)
4. ○ P(Z < 1.96)
5. ○ P₈₅
6. ● P₂₅

The correct choice likely relates to the shaded region; however, interpretation requires specific information about the shading, which appears broader than a specific z-value like those mentioned in the options.

#### Concept Review

The standard normal distribution is a key concept in statistics used to measure probabilities and understand data patterns relative to the mean and standard deviation. Understanding how to read and interpret this distribution is fundamental to analyzing statistical data.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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