Chapter 6, Problem 14P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

IQ test scores are standardized to produce a normal distribution with a mean of μ = 100 and a standard deviation of σ =15. Find the proportion of the population in each of the following IQ categories.

**a.**Genius or near genius: IQ greater than 140**b.**Very superior intelligence: IQ between 120 and 140**c.**Average or normal intelligence: IQ between 90 and 109

**a.**

To determine

**To Find:** The proportion of population in the category of genius or near to genius is over 140

Explanation

**Given info:** Score follows normal distribution with mean 100 and standard deviation 15.

And genius IQ is found to be 140.

**Calculation:**

Let
*X* respectively. Then,

Let, *p* is the probability that population’s IQ in category of genius is greater than 140 then,

The formula for finding the *z* score is,

**b.**

To determine

**To Find:** The proportion of population in the category of very superior intelligence is between when

**c.**

To determine

**To find:** The proportion of the population in category of average intelligence in between

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