Question

Assume that children's IQs follow a normal distribution with mean 100 and standard deviation of 9. Find the probability that a randomly selected child has IQ above 110.

Answer 1

Answer: 0.1335

Step-by-step explanation:

Given: Children's IQs follow a normal distribution with mean $\mu=100$ and standard deviation of $\sigma=9$.

Let X be the IQ of a random child.

The probability that a randomly selected child has IQ above 110 = P(X>100)

$=P(\dfrac{X-\mu}{\sigma}>\dfrac{110-100}{9})\\\\=P(Z>1.11)\\\\=1-P(Z<1.11)\ \ \ \ [P(Z>z)=1-P(Z<z)]\\\\=1-0.8665\\\\=0.1335\ \ \ [\text{By p-value table}]$

Hence, the probability that a randomly selected child has IQ above 110= 0.1335