Find the indicated z-score shown in the graph to the right. 0 Area = 0.0322 Z= ? Z
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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![**Title: Understanding Z-Scores and Normal Distributions**
**Introduction:**
In this exercise, we will learn how to find the z-score in a normal distribution given a specific area under the curve.
**Problem Statement:**
Find the indicated z-score shown in the graph to the right.
**Graph Description:**
The graph displays a standard normal distribution curve with a center at 0. A shaded region to the right of the curve represents an area of 0.0322. The z-score corresponding to this shaded area is unknown and marked as "z = ?".
**Guidelines:**
1. **Understand the Normal Distribution:**
- The normal distribution is a bell-shaped curve symmetric about the mean (μ = 0 for standard normal distribution).
- The total area under the curve is 1, representing the entire probability space.
2. **Identify the Area:**
- The shaded area on the graph is 0.0322. This area corresponds to the probability of the z-score being greater than the unknown value.
3. **Find the Z-Score:**
- Use statistical tables or software to find the z-score where the cumulative area to the right is 0.0322.
**Conclusion:**
Fill in the box with the z-score value rounded to two decimal places:
The z-score is [____].
(Round to two decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26146d8a-c15c-4983-bbd8-fc4fc59b6ca5%2Fec3e8e6c-b624-44ac-afe0-9284b015b427%2Fb5gtygf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Z-Scores and Normal Distributions**
**Introduction:**
In this exercise, we will learn how to find the z-score in a normal distribution given a specific area under the curve.
**Problem Statement:**
Find the indicated z-score shown in the graph to the right.
**Graph Description:**
The graph displays a standard normal distribution curve with a center at 0. A shaded region to the right of the curve represents an area of 0.0322. The z-score corresponding to this shaded area is unknown and marked as "z = ?".
**Guidelines:**
1. **Understand the Normal Distribution:**
- The normal distribution is a bell-shaped curve symmetric about the mean (μ = 0 for standard normal distribution).
- The total area under the curve is 1, representing the entire probability space.
2. **Identify the Area:**
- The shaded area on the graph is 0.0322. This area corresponds to the probability of the z-score being greater than the unknown value.
3. **Find the Z-Score:**
- Use statistical tables or software to find the z-score where the cumulative area to the right is 0.0322.
**Conclusion:**
Fill in the box with the z-score value rounded to two decimal places:
The z-score is [____].
(Round to two decimal places as needed.)
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