Answered: Based on what you have studied in this…

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

Based on what you have studied in this unit, reflect and answer the following questions:

What are the main characteristics of the normal distribution?
Why is it advantageous to use the Z scores?

For a standard normal distribution, about 68% of values falls within one standard deviation of the mean; about 95% falls within two standard deviations; and about 99.7% falls within three standard deviations. Suppose the distribution of math scores in the SAT follow a normal distribution with a mean µ=700 and a standard deviation σ=150.

Calculate the Z-score for an SAT Math score of 600. Interpret it in your own word.
Find the interval [a, b] that captures 68% of the SAT Math score in this example.
Find the interval [a, b] that captures 95% of the SAT Math score in this example.
Find the interval [a, b] that captures 99.7% of the SAT Math score in this example.

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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