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.
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
