IQ test scores are standardized to produce a normal disribution with a mean of =100 and a standard deviation of =15. Find the proportion of the population in each of the following IQ categories. a) Genius IQ over 140 b) Very intelligent IQ from 120 - 140 c) Average IQ from 90 -109 Solution Let above distribution be represented by X a) P(x>140)=1-(x-/)=1-(140-100/15)=1-(2.666)=1-.996=.004 b) P(120< x<140) =(140-100/15)-(120-100/15)=(2.666)-(1.333)=.996-.908=.088 c) P(90.

1. IQ test scores are standardized to produce a normal disribution with a mean of =100 and a
standard deviation of =15. Find the proportion of the population in each of the following IQ
categories.
a) Genius IQ over 140
b) Very intelligent IQ from 120 - 140
c) Average IQ from 90 -109
Solution
Let above distribution be represented by X
a) P(x>140)=1-(x-/)=1-(140-100/15)=1-(2.666)=1-.996=.004
b) P(120< x<140) =(140-100/15)-(120-100/15)=(2.666)-(1.333)=.996-.908=.088
c) P(90