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 the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 84$, $\mu=100$, and $\sigma = 15$.
$z=\frac{84 - 100}{15}=\frac{-16}{15}\approx - 1.07$

Step2: Find the area to the left of the z - score

We use the standard normal distribution table (or z - table). The area to the left of $z=-1.07$ is $0.1423$.

Step3: Calculate the area of the shaded region

The total area under the normal - distribution curve is 1. The area of the shaded region is $1 -$ (area to the left of $z=-1.07$).
$A = 1-0.1423=0.8577$

Answer:

$0.8577$