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 z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 100$ (mean), $\sigma = 15$ (standard deviation).
For $x = 102$, $z_1=\frac{102 - 100}{15}=\frac{2}{15}\approx0.13$.
For $x = 122$, $z_2=\frac{122 - 100}{15}=\frac{22}{15}\approx1.47$.

Step2: Use the standard normal table

We want to find $P(0.13$P(0.13From the standard - normal table, $P(Z < 1.47)=0.9292$ and $P(Z < 0.13)=0.5517$.

Step3: Calculate the probability

$P(0.13

Answer:

$0.3775$