Question

In the general population, IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of 15. Lewis Terman developed the idea of IQ and proposed classifying people with IQ scores over 140 as "genius".

1. What percent of the general population have IQ scores that would be classified as genius?

2. Give a range of values that would include IQ scores for the middle 75% of the general population.

Answer 1

Solution :

(a)

P(x > 140) = 1 - P(x < 140)

= 1 - P[(x - ) / < (140 - 100) / 15]

= 1 - P(z < 2.67)

= 0.0038

0.38%

(b)

The middle 75% has the two z values : -1.15 and +1.15 .

P(Z < -1.15) = 0.125

Using z-score formula,

x = z * +

x = -1.15 * 15 + 100 = 82.75

P(Z < 1.15) = 0.875

x = 1.15 * 15 + 100 = 117.25

Range of values are : 82.75 , 117.25