Question
Asked Sep 23, 2019
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Assume the IQ scores in a population are normally distributed with a mean value of 100 and a standard deviation of 15. Compute the proportion of people in the population for each of the following ranges of IQ scores. The answer should include hand calculations of z-scores involved.
a. less than 85
b. higher than 118
c. between 85 and 133
d. between 97 and 115

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Expert Answer

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Step 1

Given Data

Mean = 100

Standard Deviation = 15

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100 g 15 -

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Step 2

a) Less than 85

P(X < 85)

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Changing into standard normal variate 85 85 100 X и = P(Z <-1) Z < 15 P (Z NORM. S. DIST(-1, TRUE)) 1) 0.159 (From Excel 15.9% of people have IQ scores less than 85

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Step 3

b) Higher tha...

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Changing into standard normal variate 118 P 118 100 P(z > 1.2) Pz> 15 P(z > 1.2) 1 - P(z < 1.2) 1 - 0.885 0.115 (P(z1.2) 0.885(From Excel NORM. S. DIST(1.2, TRUE)) 11.5% of people have IQ scores higher than 118

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