Question

find the indicated iq score. 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 indicated iq score, x, is . (round to the nearest whole number as needed.)

Explanation:

Step1: Find the z - score

We know that the area to the left of the value $x$ is $0.8$. Looking up this value in the standard normal distribution table (z - table), the z - score corresponding to an area of $0.8$ is approximately $z = 0.84$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 100$ (mean), $\sigma = 15$ (standard deviation), and $z$ is the z - score. We want to solve for $x$. Rearranging the formula gives $x=\mu + z\sigma$.
Substitute $\mu = 100$, $z = 0.84$, and $\sigma = 15$ into the formula:
$x=100+0.84\times15$.
$x = 100+12.6$.
$x=112.6$.

Answer:

$113$