---**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.---

Answered: Find two z values so that 56% of the…

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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Question

---

**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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