Question

IQ test scores are standardized to produce a normaldistribution with a mean of 100 and a standarddeviation of 15. Find the proportion of the popula-tion in each of the following IQ categories.Gartea. Average or normal intelligence: IQ from 90 to 109

Answer 1

Answer:

Explanation:

The mean, µ = 100

The standard deviation, σ = 15

At X = 90, the z-score is calculated below

$\begin{gathered} z=\frac{X-\mu}{\sigma} \\ \\ z=\frac{90-100}{15} \\ \\ z=-\frac{10}{15} \\ \\ z=-0.67 \end{gathered}$

At X = 109

$\begin{gathered} z=\frac{109-90}{15} \\ \\ z=\frac{19}{15} \\ \\ z=1.27 \end{gathered}$

P(90 < X < 109) = P(-0.67 < z < 1.27)

From the standard normal

P(-0.67

The proportion of the population with IQ from 90 to 109 = 0.64653 x 100% = 64.65%