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1. The scores on a test have a mean of 100 and a standard deviation of 15. If a personnel manager wishes to select from the top 75% of applicants who take the test, find the cutoff score.

1. The scores on a test have a mean of 100 and a standard deviation of 15. If a personnel manager wishes to select from the top 75% of applicants who take the test, find the cutoff score.

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
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**Statistics and Data Analysis Problems** 1. **Test Score Selection** The scores on a test have a mean of 100 and a standard deviation of 15. If a personnel manager wishes to select from the top 75% of applicants who take the test, find the cutoff score. 2. **Charitable Contributions Analysis** The average charitable contribution itemized per income tax return in Pennsylvania is $792. Suppose that... (continued text not visible). --- *Explanation of Concepts:* - **Mean**: The average of all data points. - **Standard Deviation**: Measures the dispersion of data points from the mean. *Example Calculation*: To find the cutoff score for the top 75% of applicants, you can use the following steps: 1. Determine the Z-score corresponding to the 25th percentile (since you want the top 75%). 2. Apply the Z-score formula: \( X = \mu + Z\sigma \). Where: - \( X \) is the cutoff score, - \( \mu \) is the mean, - \( Z \) is the Z-score. - \( \sigma \) is the standard deviation. Refer to a Z-table to find the Z-score for the 25th percentile (approximately -0.674). Example calculation: \( X = 100 + (-0.674 \times 15) \) \( X = 100 - 10.11 \) \( X \approx 89.89 \) *Cutoff score*: Approximately 90 (to be from the top 75%).
Transcribed Image Text:**Statistics and Data Analysis Problems** 1. **Test Score Selection** The scores on a test have a mean of 100 and a standard deviation of 15. If a personnel manager wishes to select from the top 75% of applicants who take the test, find the cutoff score. 2. **Charitable Contributions Analysis** The average charitable contribution itemized per income tax return in Pennsylvania is $792. Suppose that... (continued text not visible). --- *Explanation of Concepts:* - **Mean**: The average of all data points. - **Standard Deviation**: Measures the dispersion of data points from the mean. *Example Calculation*: To find the cutoff score for the top 75% of applicants, you can use the following steps: 1. Determine the Z-score corresponding to the 25th percentile (since you want the top 75%). 2. Apply the Z-score formula: \( X = \mu + Z\sigma \). Where: - \( X \) is the cutoff score, - \( \mu \) is the mean, - \( Z \) is the Z-score. - \( \sigma \) is the standard deviation. Refer to a Z-table to find the Z-score for the 25th percentile (approximately -0.674). Example calculation: \( X = 100 + (-0.674 \times 15) \) \( X = 100 - 10.11 \) \( X \approx 89.89 \) *Cutoff score*: Approximately 90 (to be from the top 75%).
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