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: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 100$ (mean), $\sigma = 15$ (standard deviation). 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 z - table

We use the standard normal distribution table. The area to the left of $z_1=-1.33$ is $0.0918$ and the area to the left of $z_2 = 0.67$ is $0.7486$.

Step3: Find the shaded area

The area of the shaded region is $A=\text{Area}(z = 0.67)-\text{Area}(z=-1.33)$. $A = 0.7486-0.0918=0.6568$.

Answer:

$0.6568$