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

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((X-\mu)/(\sigma)>(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