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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

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 i.e.X>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 μ and σ be the mean and standard deviation of score X respectively. Then,

μ=100σ=15

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

p=P(X>140)=1P(X<140)

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 X>120 & X<140

c.

To determine

To find: The proportion of the population in category of average intelligence in between X>90 & X<109.

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