Question

find the area of the shaded region. 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 area of the shaded region is (round to four decimal places as needed).

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu = 100$ (mean), $\sigma = 15$ (standard deviation).
For $x = 102$, $z_1=\frac{102 - 100}{15}=\frac{2}{15}\approx0.1333$.
For $x = 132$, $z_2=\frac{132 - 100}{15}=\frac{32}{15}\approx2.1333$.

Step2: Use the standard normal distribution table

We want to find $P(0.1333We know that $P(0.1333From the standard - normal table, $P(Z < 2.1333)\approx0.9835$ and $P(Z < 0.1333)\approx0.5517$.

Step3: Calculate the probability

$P(0.1333

Answer:

$0.4318$