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%.

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:



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:



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