Question

Assume that adults have iq scores that are normally distributed with a mean of 100100 and a standard deviation of 15. find the third quartile upper q 3q3​, which is the iq score separating the top​ 25% from the others.

Answer 1

The bell curve attached below shows the normal distribution of the data.

We are looking the value of X such as the area to its left gives the probability of 0.75

We first need the z-score which we can obtain by reading from the z-table (as shown in the second picture below)

The z-score is = 0.7734

Then we use the following formula to work out X
z-score = (X - Mean) ÷ Standard Deviation
0.7734 = (X - 100) ÷ 15
0.7734×15 = X - 100
11.601 = X - 100
X = 11.601 + 100
X = 111.601 ≈ 112 

Hence the third quartile is 112