**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%).

Answered: 1. The scores on a test have a mean of…

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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1. According to one study, the average hours of sleep on a weeknight for men was 6.9 hours with a standard deviation of 1.5 hours. a. Find the proportion of men who sleep for more than 8 hours per night. b. Find the proportion of men who sleep for less than 6 hours per night. c. Find the proportion of men who sleep between 6-8 hours per night. d. Find the number of hours that represents the 90th percentile.
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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.