Find two z values so that 56% of the middle area is bounded by them. Use O The Standard Normal Distribution Table and enter the answers rounded to- decimal places, separated by a comma if needed.
Find two z values so that 56% of the middle area is bounded by them. Use O The Standard Normal Distribution Table and enter the answers rounded to- decimal places, separated by a comma if needed.
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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![---
**Finding Z-Values for a Given Middle Area**
To determine the z-values that bound the middle 56% of a standard normal distribution, follow these steps:
1. **Understanding the Problem:**
- You're tasked to find two z-values such that the area between them under the standard normal curve is 56%.
2. **Use of the Standard Normal Distribution Table:**
- Refer to the Standard Normal Distribution Table to find the critical z-values. This table provides the area under the curve to the left of a given z-value.
3. **Calculation Steps:**
- Since the middle area is 56%, the remaining area in the tails is 44%.
- This 44% is split equally between the lower and upper tails, so each tail has 22% (0.22) of the total area.
- Find the z-value for the area of 0.22 in the tail. Since the table gives the cumulative area from the left, look for the z-value with 0.22 to the left of it.
- The same logic applies to the upper tail, but symmetry of the standard normal distribution allows us to use positive and negative z-values of the same magnitude.
4. **Input Your Answer:**
- Once you find the z-values, round them to two decimal places and enter them separated by a comma.
**System Interface for Answers:**
- The input box on the screen is labeled as `z =` where you need to input the two z-values.
- There is an additional pop-up feature to facilitate complex notations or multiple entries.
**Interface Options:**
- You have buttons labeled `Check`, `Save For Later`, and `Submit Assignment` for interaction.
Please use the following format to input your final answers:
```
z = -a, b
```
Where `-a` and `b` are the calculated z-values rounded to two decimal places.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea0820f3-64e4-4dfd-b401-c1fa00677880%2Fa23f5092-736d-446f-8fed-d040c4c40b4c%2Fbbindjg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
**Finding Z-Values for a Given Middle Area**
To determine the z-values that bound the middle 56% of a standard normal distribution, follow these steps:
1. **Understanding the Problem:**
- You're tasked to find two z-values such that the area between them under the standard normal curve is 56%.
2. **Use of the Standard Normal Distribution Table:**
- Refer to the Standard Normal Distribution Table to find the critical z-values. This table provides the area under the curve to the left of a given z-value.
3. **Calculation Steps:**
- Since the middle area is 56%, the remaining area in the tails is 44%.
- This 44% is split equally between the lower and upper tails, so each tail has 22% (0.22) of the total area.
- Find the z-value for the area of 0.22 in the tail. Since the table gives the cumulative area from the left, look for the z-value with 0.22 to the left of it.
- The same logic applies to the upper tail, but symmetry of the standard normal distribution allows us to use positive and negative z-values of the same magnitude.
4. **Input Your Answer:**
- Once you find the z-values, round them to two decimal places and enter them separated by a comma.
**System Interface for Answers:**
- The input box on the screen is labeled as `z =` where you need to input the two z-values.
- There is an additional pop-up feature to facilitate complex notations or multiple entries.
**Interface Options:**
- You have buttons labeled `Check`, `Save For Later`, and `Submit Assignment` for interaction.
Please use the following format to input your final answers:
```
z = -a, b
```
Where `-a` and `b` are the calculated z-values rounded to two decimal places.
---
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