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:
[tex]z= \frac{x-u}{s} [/tex]
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: