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:
[tex]-0.674= \frac{x-99.5}{20.6} \\ \\
x=85.6[/tex]
Rounding to one decimal point, 85.6 is the value of first quartile.
