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. click to view page 1 of the table. click to view page 2 of the table. 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 $x = 70$, $\mu=100$, and $\sigma = 15$. So, $z=\frac{70 - 100}{15}=\frac{- 30}{15}=-2$.

Step2: Find the area from the z - table

We want to find the area to the left of $z=-2$ in the standard normal distribution. Looking up $z = - 2$ in the standard - normal table (z - table), the area corresponding to $z=-2$ is $0.0228$.

Answer:

$0.0228$