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

Explanation:

Step1: Find the area to the left of x

The area to the right of x is 0.2119. So the area to the left of x, denoted as $A$, is $A = 1 - 0.2119=0.7881$.

Step2: Use the z - score table

Looking up the area 0.7881 in the standard normal distribution z - score table, the corresponding z - score, $z$, is approximately 0.80.

Step3: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 100$ (mean) and $\sigma = 15$ (standard deviation). We know $z = 0.80$, $\mu=100$, and $\sigma = 15$. Rearranging the formula for $x$ gives $x=\mu + z\sigma$.
Substitute the values: $x=100+0.80\times15$.
$x = 100 + 12$.
$x=112$.

Answer:

112