SOLUTION: IQ test scores are standardized to produce a normal distribution with a mean of u=100 and a standard deviation of 0=15. Find the proportion of the population in each of the foll

Algebra ->  Probability-and-statistics -> SOLUTION: IQ test scores are standardized to produce a normal distribution with a mean of u=100 and a standard deviation of 0=15. Find the proportion of the population in each of the foll      Log On


   

Question 387978: IQ test scores are standardized to produce a normal
distribution with a mean of u=100 and a standard
deviation of 0=15. Find the proportion of the population
in each of the following IQ categories.
a. Genius or near genius: IQ over 140
b. Very superior intelligence: IQ from 120 to 140
c. Average or normal intelligence: IQ from 90 to 109
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

*Note: z+=+blue%28x+-+mu%29%2Fblue%28sigma%29   mu = 100, sigma= 15

Converting z score to a P decimal using the manner You choose to find percentage

a. Genius or near genius: IQ over 140 

  z > 40/15 = 2.6667 P(z > 2.6667) = .0038  3.8%  of the population

b. Very superior intelligence: IQ from 120 to 140  (z = 20/15 and z = 40/15)

 P( 1.333 < z <2.6667) = .0874    8.74% of the population

c. Average or normal intelligence: IQ from 90 to 109 (z = 9/15 and z = -10/15)

 ( - .6667 < z < .6) = .4733   47.33% of the population