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 $x = 91$, $\mu=100$, and $\sigma = 15$. So $z=\frac{91 - 100}{15}=\frac{-9}{15}=- 0.6$.

Step2: Find the area from the z - table

We want to find the area to the right of $z=-0.6$ under the standard normal curve. The total area under the standard - normal curve is 1. The area to the left of $z =-0.6$ from the standard normal table is $0.2743$. So the area to the right of $z=-0.6$ is $1 - 0.2743=0.7257$.

Answer:

$0.7257$