Question

Assume that adults have IQ scores that are normally distributed with a mean of 99.5 and a standard deviation 20.6. Find the first quartile Upper Q 1​, which is the IQ score separating the bottom​ 25% from the top​ 75%.

Answer 1

Population Mean = u = 99.5
Population standard Deviation = s = 20.6
We want to find the first Quartile Q1 which is the value with 0.25 percentile score.

First we will find the z value corresponding to 0.25 percentile. From the z table this value comes out to be z = -0.674

The formula to calculate z score is:

$z= \frac{x-u}{s}$

We want to find the value of x. This is the value of First Quartile Q1. Using the values in the above equation, we get:

$-0.674= \frac{x-99.5}{20.6} \\ \\ x=85.6$

Rounding to one decimal point, 85.6 is the value of first quartile.