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 $\mu = 100$ (mean), $\sigma = 15$ (standard deviation). For $x = 70$, $z_1=\frac{70 - 100}{15}=\frac{- 30}{15}=-2$. For $x = 105$, $z_2=\frac{105 - 100}{15}=\frac{5}{15}\approx0.33$.

Step2: Use standard normal table

We want to find $P(-2

Step3: Calculate the probability

$P(-2

Answer:

$0.6065$