### Finding the Z-Value for a Given Area in a Standard Normal Distribution#### Instructions:1. **Objective**: Find the z value that corresponds to the given area in the figure.2. **Resources**: Use the [Standard Normal Distribution Table](#) to find the z-value.3. **Requirements**: Enter your answer to two decimal places.#### Visualization:The diagram provided is a bell curve representing the standard normal distribution. Key elements of the diagram include:- **Bell Curve**: A symmetrical, bell-shaped curve centered on the mean (µ = 0) with a standard deviation (σ = 1).- **Area under the Curve**: The shaded area to the right of the mean is labeled 0.9875. This represents the cumulative probability from the mean to z.- **Mean and Symmetry**: The red vertical line in the center marks the mean (0).#### Steps:1. **Identify the given area**: The area to the left of the distribution is 0.9875.2. **Look Up the Z-Value**: Use the Standard Normal Distribution Table to find the z-value that corresponds to a cumulative probability of 0.9875.3. **Enter Answer**: Input the z-value in the designated box with two decimal precision.#### Example:For an area of 0.9875, you can find the corresponding z-value using the z-table, which in this case, should be approximately 2.26.#### Interactive Check:After computing, click the “Check” button to verify your answer.#### Saving Progress:Use the “Save For Later” button if you wish to retain your progress and continue at another time.*Note: The given figure is a conceptual illustration and is not drawn to scale.*---This exercise aims to build your understanding of using standard normal distribution tables to find specific z-values based on given probabilities.

The standard normal variable z follows normal distribution with mean 0 and standard deviation 1.

Find the z value that corresponds to the glven area In the figure below. Use O The Standard Normal Distribution Table and enter the answer to 2 decimal places. (Note: Flgure not drawn to scale.) + 0.9875

Find the z value that corresponds to the glven area In the figure below. Use O The Standard Normal Distribution Table and enter the answer to 2 decimal places. (Note: Flgure not drawn to scale.) + 0.9875

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

### Finding the Z-Value for a Given Area in a Standard Normal Distribution

#### Instructions:
1. **Objective**: Find the z value that corresponds to the given area in the figure.
2. **Resources**: Use the [Standard Normal Distribution Table](#) to find the z-value.
3. **Requirements**: Enter your answer to two decimal places.

#### Visualization:
The diagram provided is a bell curve representing the standard normal distribution. Key elements of the diagram include:

- **Bell Curve**: A symmetrical, bell-shaped curve centered on the mean (µ = 0) with a standard deviation (σ = 1).
- **Area under the Curve**: The shaded area to the right of the mean is labeled 0.9875. This represents the cumulative probability from the mean to z.
- **Mean and Symmetry**: The red vertical line in the center marks the mean (0).

#### Steps:

1. **Identify the given area**: The area to the left of the distribution is 0.9875.
2. **Look Up the Z-Value**: Use the Standard Normal Distribution Table to find the z-value that corresponds to a cumulative probability of 0.9875.
3. **Enter Answer**: Input the z-value in the designated box with two decimal precision.

#### Example:
For an area of 0.9875, you can find the corresponding z-value using the z-table, which in this case, should be approximately 2.26.

#### Interactive Check:
After computing, click the “Check” button to verify your answer.

#### Saving Progress:
Use the “Save For Later” button if you wish to retain your progress and continue at another time.

*Note: The given figure is a conceptual illustration and is not drawn to scale.*

---

This exercise aims to build your understanding of using standard normal distribution tables to find specific z-values based on given probabilities.

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