Question

Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. The indicated IQ score, x, is _______

0.9

Answer 1

Solution:

The IQ scores are normally distributed with mean μ=100 and standard deviation σ = 15.
The x value in the graph covers the area of 0.9 to the right of the curve.
The z score obtained at the point of x is
P(Z < z) = 0.9
=> P(Z ≤ z) = 1-0.9
=> P(Z ≤ z) = 0.1
P(z) = 0.1
z = -1.28

Using z-score formula,
x = z * σ + μ
x = -1.28 * 15 + 100 = 80.8

The indicated IQ score, x is 80.8