Homework Help is Here – Start Your Trial Now!
Math
Statistics
Assuming a normal curve, find the lowest Z score a person could have while being in the following top percentages of a country in mathematics ability. (a) 10% (b) 5%

Assuming a normal curve, find the lowest Z score a person could have while being in the following top percentages of a country in mathematics ability. (a) 10% (b) 5%

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
**Title: Understanding Z-Scores in Mathematics Ability** **Description:** In the context of a normal distribution curve, this exercise involves calculating the lowest Z-score needed for a person to be in certain top percentages regarding mathematics ability within a country. **Problem Statement:** **Objective:** Determine the lowest Z-score a person must achieve to be included in the specified top percentages. **Percentages to Consider:** (a) Top 10% (b) Top 5% **Instruction:** Utilize the properties of the normal distribution and corresponding Z-score tables to find the necessary scores for the given percentiles. **Concept Explanation:** The Z-score represents how many standard deviations an element is from the mean. By using a Z-score table (or calculator), you can find the exact value that corresponds to the top percentage cutoffs in a normally distributed data set. **Application:** Such calculations can help in understanding benchmarks in educational assessments and setting realistic goals for student performance evaluations.
Transcribed Image Text:**Title: Understanding Z-Scores in Mathematics Ability** **Description:** In the context of a normal distribution curve, this exercise involves calculating the lowest Z-score needed for a person to be in certain top percentages regarding mathematics ability within a country. **Problem Statement:** **Objective:** Determine the lowest Z-score a person must achieve to be included in the specified top percentages. **Percentages to Consider:** (a) Top 10% (b) Top 5% **Instruction:** Utilize the properties of the normal distribution and corresponding Z-score tables to find the necessary scores for the given percentiles. **Concept Explanation:** The Z-score represents how many standard deviations an element is from the mean. By using a Z-score table (or calculator), you can find the exact value that corresponds to the top percentage cutoffs in a normally distributed data set. **Application:** Such calculations can help in understanding benchmarks in educational assessments and setting realistic goals for student performance evaluations.
Expert Solution
Step 1

Using Normal curve

Z = x-μσ

We have given :

( a ) 10%

P ( Z < z ) = 0.10

Using Excel

= NORMSINV(0.10)

= -1.281

ANSWER : ZSCORE = -1.281

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS