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

Answer:

A. 16th

Step-by-step 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.

$z=\frac{x-\mu}{\sigma}$, where,

z = Z-score,

x = Sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

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

$z=\frac{85-100}{15}$

$z=\frac{-15}{15}$

$z=-1$

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

Using normal distribution table, we will get:

$P(z$

Let us convert 0.15866 into percentage as:

$0.15866\times 100\%=15.866\%\approx 16\%$

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