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. 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. 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 $x = 102$, $z_1=\frac{102 - 100}{15}=\frac{2}{15}\approx0.1333$. For $x = 126$, $z_2=\frac{126 - 100}{15}=\frac{26}{15}\approx1.7333$.

Step2: Use the standard normal table

We want to find $P(0.1333<Z<1.7333)$. $P(0.1333<Z<1.7333)=P(Z < 1.7333)-P(Z < 0.1333)$. From the standard - normal table, $P(Z < 1.7333)\approx0.9582$ and $P(Z < 0.1333)\approx0.5517$.

Step3: Calculate the probability

$P(0.1333<Z<1.7333)=0.9582 - 0.5517=0.4065$.

Answer:

$0.4065$