Question

On a normal distribution if IQ test scores, with a mean of 100 and a standard deviation of 15 points, a score of 85 places you approximately in what percentile of the population?A. 16thB. 50thC. 97thD. 76thE. 24th

Answer 1

A. 16th

Explanation:

We have been given that on a normal distribution IQ test scores, with a mean of 100 and a standard deviation of 15 points. We are asked to find the percentile for a score of 85.

We will use z-score formula and normal distribution table to answer our given problem.

`z=(x-\mu)/(\sigma)`, where,

z = Z-score,

x = Sample score,

`\mu` = Mean,

`\sigma` = Standard deviation.

Upon substituting our given values in z-score formula, we will get:

`z=(85-100)/(15)`

`z=(-15)/(15)`

`z=-1`

Now, we need to find area under a normal curve that corresponds to z-score of
`-1` that is
`P(z<-1)`.

Using normal distribution table, we will get:

`P(z<-1)=0.15866`

Let us convert 0.15866 into percentage as:

`0.15866* 100\%=15.866\%\approx 16\%`

Therefore, a score of 85 places you approximately in 16th percentile of the population.