Question

Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with μ=101 and σ=24. (a) what proportion of children aged 13 to 15 years old have scores on this test above 83 ? (note: please enter your answer in decimal form. for example, 45.23% should be entered as 0.4523.)

Answer 1

The probability is 0.7734.

The z-score for this value is given by:

z =(X-μ)/σ = (83-101)/24 = -18/24 = -0.75.

Using a z-table (http://www.z-table.com) we see that the area to the left of this (lower than) is 0.2266.  We want the percentage that will score higher on the test, so we subtract fro 1:
1 - 0.2266 = 0.7734.