Answered: The median ACT scores for four-year…

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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Question

The median ACT scores for four-year colleges to follow normal distribution with a mean of 24 points and a standard deviation of 4. We look at the distribution of means of the MidACT variable for samples of 150 colleges at a time. a) using the normal distribution for MidACT, what proportion of colleges should have MidACT of 26 or higher? b) what proportion of samples of 100 colleges would give a sample mean of MidACT of 26 or higher? c) would the results of part a and part b still be appropriate if the distribution of MidACT values for the population of all four-year colleges was actually right-skewed( but still had a mean of 24 and standard deviation of 4)?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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