Question

Given IQ scores are approximately normally distributed with a mean of 100 and standard deviation of 15, the proportion of people with IQs above 130 is:

Answer 1

Answer: 0.0228 .

Explanation:

Given, IQ scores are approximately normally distributed with a mean of 100 and standard deviation of 15

Let X denotes the IQ score.

Then, the proportion of people with IQs above 130 is

`P(X>130)=P((X-mean)/( standard\ deviation)>(130-100)/(15))\\\\= P(Z>2)\ \ \ \[Z=(X-mean)/( standard\ deviation)]`

`=1-P(Z<2)\ \ \ [P(Z>z)=1-P(Z<z)]\\\\=1-0.9772\ [\text{By z table}]\\\\=0.0228`

Hence, the proportion of people with IQs above 130 is 0.0228 .