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 z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set.
For $x = 95$, $z_1=\frac{95 - 100}{15}=\frac{- 5}{15}\approx - 0.33$.
For $x = 120$, $z_2=\frac{120 - 100}{15}=\frac{20}{15}\approx1.33$.

Step2: Use the standard normal table

We want to find $P(-0.33We know that $P(-0.33From the standard - normal table, $P(Z < 1.33)=0.9082$ and $P(Z < - 0.33)=0.3707$.

Step3: Calculate the probability

$P(-0.33

Answer:

$0.5375$