Question

If mean IQ is `105` and standard deviation is `20`, what is the probability that a randomly selected adult has an IQ between `85` and `125`?

Answer 1

The probability that that a randomly selected adult has an IQ between 85 and 125 is `0.6826` or `68.26%`

Explanation:

As mean IQ is `mu=105` and standard deviation is `sigma=20`,

the `z`-score for `85` is `(85-105)/20=-1`

and `z`-score for `125` is `(125-105)/20=1`

As normal curve is symmetrically distributed and from tables the probability for `z=1` is `0.3413`

and hence probability that a randomly selected adult has an IQ between 85 and 125 i.e. between `z=-1` and `z=+1` is `0.3413xx2=0.6826`

Hence, the probability that that a randomly selected adult has an IQ between 85 and 125 is `0.6826` or `68.26%`