**Finding the Z-Value Corresponding to an Area**On this educational page, we will learn how to find the z value that corresponds to a given area under the standard normal distribution curve.### Problem Statement**"Find the z value that corresponds to the given area in the figure below. Use The Standard Normal Distribution Table and enter the answer to 2 decimal places."**(Note: Figure not drawn to scale).### Explanation of the Graph- **Normal Distribution Curve**: The image shows a bell-shaped curve, which represents the standard normal distribution.- **Highlighted Area**: The shaded area under the curve is marked with a value of **0.7764**, which likely represents the cumulative area to the left of a certain z value.- **Axes**: - The horizontal axis (x-axis) is marked with **z**, which represents the z-values or standard scores. - The vertical axis (y-axis) denotes the probability density function values.- **Vertical Line**: There is a red vertical line extending from the x-axis up to the curve.### Steps to Solve1. **Identify the Area**: According to the figure, the area to the left of the z value is 0.7764.2. **Refer to the Standard Normal Distribution Table**: Use this table to find the z value that corresponds to a cumulative probability of 0.7764.3. **Determine the Z-Value**: Locate the value in the z-table and ensure to round it to two decimal places.### Input BoxBelow the graph, there is a section to input the calculated z value with a text field labeled `z =`. After determining the correct z value, enter it into this field.### Check Your AnswerFinally, there is a "Check" button to verify if the entered z value is correct. Additionally, options to "Save For Later" or "Submit Assignment" are provided.### NoteThe authenticity of the standard normal distribution table and correct referencing is critical for solving this example accurately.

Answered: Image /qna-images/answer/5f83703a-b8e9-4f2f-bed0-34cfac756490.jpg

X 1 v 4 v 5 v 6 v 8 10 X 13 The Standard Normal Distribution Table and enter the answer to 2 decimal places. Find the z value that corresponds to the glven area In the figure below. Use (Note: Flgure not drawn to scale.) + 0.7764

X 1 v 4 v 5 v 6 v 8 10 X 13 The Standard Normal Distribution Table and enter the answer to 2 decimal places. Find the z value that corresponds to the glven area In the figure below. Use (Note: Flgure not drawn to scale.) + 0.7764

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 Corresponding to an Area**

On this educational page, we will learn how to find the z value that corresponds to a given area under the standard normal distribution curve.

### Problem Statement
**"Find the z value that corresponds to the given area in the figure below. Use The Standard Normal Distribution Table and enter the answer to 2 decimal places."**
(Note: Figure not drawn to scale).

### Explanation of the Graph

- **Normal Distribution Curve**: The image shows a bell-shaped curve, which represents the standard normal distribution.
- **Highlighted Area**: The shaded area under the curve is marked with a value of **0.7764**, which likely represents the cumulative area to the left of a certain z value.
- **Axes**:
- The horizontal axis (x-axis) is marked with **z**, which represents the z-values or standard scores.
- The vertical axis (y-axis) denotes the probability density function values.
- **Vertical Line**: There is a red vertical line extending from the x-axis up to the curve.

### Steps to Solve

1. **Identify the Area**: According to the figure, the area to the left of the z value is 0.7764.
2. **Refer to the Standard Normal Distribution Table**: Use this table to find the z value that corresponds to a cumulative probability of 0.7764.
3. **Determine the Z-Value**: Locate the value in the z-table and ensure to round it to two decimal places.

### Input Box

Below the graph, there is a section to input the calculated z value with a text field labeled `z =`. After determining the correct z value, enter it into this field.

### Check Your Answer

Finally, there is a "Check" button to verify if the entered z value is correct. Additionally, options to "Save For Later" or "Submit Assignment" are provided.

### Note

The authenticity of the standard normal distribution table and correct referencing is critical for solving this example accurately.

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