Find the z-score for which 80% of the distribution's area lies to its right.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Question: Finding the Z-Score for a Given Area
**Problem Statement:**
Find the z-score for which 80% of the distribution's area lies to its right.
**Options:**
1. -1.84
2. -2.16
3. -0.84
4. -0.52
---
**Solution:**
To find the z-score for which 80% of the distribution's area lies to its right, you need to refer to the standard normal distribution table (Z-table) or use a calculator that provides the cumulative probability from the left.
1. Know that if 80% of the distribution's area lies to the right, then 20% of the area lies to the left.
2. Look up for the z-score where the cumulative probability is 0.20 (20%) in the Z-table.
3. The corresponding z-score is approximately -0.84.
Therefore, the correct answer is:
**Option C: -0.84**
---
**Explanation of Diagrams/Buttons:**
There is a graphical user interface showing a multiple-choice question. A user has selected the option -1.84. There is also a button with an 'X' mark in the center and a circular arrow, often representing the 'Clear' or 'Reset' option to choose a different answer.
---
**Key Concepts:**
- **Z-Score**: A Z-score indicates how many standard deviations an element is from the mean.
- **Standard Normal Distribution**: A normal distribution with a mean of 0 and a standard deviation of 1.
- **Z-Table**: A table that provides the area (or probability) under the curve of the standard normal distribution to the left of a given z-score.
Visit our resources page for a detailed tutorial on understanding and utilizing the Z-table.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea0820f3-64e4-4dfd-b401-c1fa00677880%2F9ecab953-097a-4b78-b9de-a78fc2d9bf50%2Fowju14p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question: Finding the Z-Score for a Given Area
**Problem Statement:**
Find the z-score for which 80% of the distribution's area lies to its right.
**Options:**
1. -1.84
2. -2.16
3. -0.84
4. -0.52
---
**Solution:**
To find the z-score for which 80% of the distribution's area lies to its right, you need to refer to the standard normal distribution table (Z-table) or use a calculator that provides the cumulative probability from the left.
1. Know that if 80% of the distribution's area lies to the right, then 20% of the area lies to the left.
2. Look up for the z-score where the cumulative probability is 0.20 (20%) in the Z-table.
3. The corresponding z-score is approximately -0.84.
Therefore, the correct answer is:
**Option C: -0.84**
---
**Explanation of Diagrams/Buttons:**
There is a graphical user interface showing a multiple-choice question. A user has selected the option -1.84. There is also a button with an 'X' mark in the center and a circular arrow, often representing the 'Clear' or 'Reset' option to choose a different answer.
---
**Key Concepts:**
- **Z-Score**: A Z-score indicates how many standard deviations an element is from the mean.
- **Standard Normal Distribution**: A normal distribution with a mean of 0 and a standard deviation of 1.
- **Z-Table**: A table that provides the area (or probability) under the curve of the standard normal distribution to the left of a given z-score.
Visit our resources page for a detailed tutorial on understanding and utilizing the Z-table.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman