find the area of the shaded region. the graph to the right depicts iq scores of adults, and those scores are…

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.)

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.)

Answer

Explanation:

Step1: Standardize the values

We use the z - score formula $z=\frac{x-\mu}{\sigma}$, where $\mu = 100$ (mean), $\sigma=15$ (standard deviation). Let's assume the lower - bound of the shaded region is $x_1$ and the upper - bound is $x_2$. If we assume the shaded region is from $x = 80$ to $x = 110$: For $x = 80$, $z_1=\frac{80 - 100}{15}=\frac{- 20}{15}\approx - 1.33$. For $x = 110$, $z_2=\frac{110 - 100}{15}=\frac{10}{15}\approx0.67$.

Step2: Use the standard normal table

We look up the values in the standard - normal table (z - table). The area to the left of $z_1=-1.33$ is $A_1 = 0.0918$ and the area to the left of $z_2 = 0.67$ is $A_2=0.7486$.

Step3: Calculate the area of the shaded region

The area of the shaded region $A=A_2 - A_1$. $A=0.7486-0.0918 = 0.6568$.

Answer:

$0.6568$