Answered: The results of a certain intelligence…

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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The results of a certain intelligence quotient (IQ) test are distributed according to the normal distribution, the mean of which is 100 and the standard deviation of 16. If such a test is administered, the proportion p of individuals whose IQ is between a and b is given by (see image).

Use the first three terms of the appropriate Maclaurin series to estimate the proportion of individuals with an IQ between 100 and 116.

p=
1
2πT
b - 100
Sa
16
a-100
16
e
-X
2
2 dx

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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