Answer to Question #341118 in Statistics and Probability for Himanshi

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.