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 indicated value is 0.89. Looking up 0.89 in the standard normal distribution table (z - table), the corresponding z - score is approximately $z = 1.23$.

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 we want to find $x$. Rearranging the formula for $x$ gives $x=\mu+z\sigma$.
Substitute $\mu = 100$, $z = 1.23$, and $\sigma = 15$ into the formula: $x=100 + 1.23\times15$.

Step3: Calculate the value of x

$x=100+18.45=118.45$.

Answer:

118