Question

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Determine the 90th percentile for IQ scores

Answer 1

Solution:

We are given,

mean = = 100

SD = = 15

First, we need to translate the problem into an area or probability. we can say the kth percentile of a set of data divides the lower k% of a data set from the upper (100-k)%. So the 90th percentile divides the lower 90% from the upper 10% - That is it has about 90% below and about 10% above.

Hence we have to find z for area 0.1

Using excel , =NORMSINV(0.1)

So, z = -1.28

Formula for finding IQ score is,

IQ score = = 100 - (-1.28)* 15

IQ score = 119

Therefore, the 90th percentile for IQ scores is about 119.

Done