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 z - score

We know that the area to the right of the value $x$ is $0.1020$. So the area to the left of $x$ is $A = 1 - 0.1020=0.8980$. Looking up this area in the standard - normal distribution table (z - table), the corresponding z - score $z$ is approximately $1.27$.

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 $\mu = 100$, $z = 1.27$, and $\sigma = 15$ into the formula: $x=100+1.27\times15$.

Step3: Calculate the value of $x$

$x = 100+1.27\times15=100 + 19.05=119.05$.

Answer:

119