Question

IQs are designed to be N(100,225).

a. To join Mensa an IQ of 138 is required. What percentage of the population are

eligible to join?

b. A psychologist claims that any child with an IQ of 150+ is ‘gifted’. How many ‘gifted’ children would you expect to find in a school of 1800 pupils?

Answer 1

a.

$$P(X\ge 138)=1-P(Z<\dfrac{138-100}{\sqrt{225}})$$

$$\approx1-P(Z<2.533)\approx0.00565$$

b.

$$P(X\ge 150)=1-P(Z<\dfrac{150-100}{\sqrt{225}})$$

$$\approx1-P(Z<2.533)\approx0.000429$$

$0.000429(1800)=1$ ‘gifted’ child.