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 112 (round to the nearest whole number as needed.)

Explanation:

Step1: Use z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. We need to find the z - score corresponding to the area to the left of $x$ under the normal curve. Given the area to the left is $0.79$. Looking up in the standard normal distribution table (z - table), the z - score $z$ corresponding to an area of $0.79$ is approximately $0.81$.

Step2: Rearrange the z - score formula to solve for $x$

Starting with $z=\frac{x - \mu}{\sigma}$, we can multiply both sides by $\sigma$ and then add $\mu$ to get $x=\mu+z\sigma$. We know that $\mu = 100$, $\sigma=15$, and $z = 0.81$.

Step3: Calculate the value of $x$

Substitute the values into the formula: $x=100 + 0.81\times15=100+12.15 = 112.15$. Rounding to the nearest whole number, we get $x = 112$.

Answer:

$112$