Question

The IQs of a large population is normally distributed with a mean of 100 and an SD of 15 points. Suppose you randomly choose 40 people from the population. What is the approximate chance that you get at least one person with an IQ of 130 or higher?

Answer 1

Explanation:

Given that the IQs of a large population is normally distributed with a mean of 100 and an SD of 15 points.

Sample size n =40

Std error of sample =
`(\sigma)/(√(n) ) =(15)/(√(40) ) = 2.37`

the approximate chance that you get exactly one person with an IQ of 130 or higher

=P(X>130)= P(Z>2) = 0.025

Since each person is independent of the other and there are only two outcomes, we get X no of persons in 40 group having iq >30 is binomial.

the approximate chance that you get at least one person with an IQ of 130 or higher=1-no one is having iq >130

=1-0.025^40

=almost 1.

=