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

Since the area to the right of \(x\) is \(0.0912\), the area to the left of \(x\) is \(1 - 0.0912=0.9088\).
Using the standard normal distribution table (or a calculator with a normal - distribution function), the \(z\) - score corresponding to an area of \(0.9088\) is \(z = 1.33\).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 100\), \(\sigma = 15\), and \(z = 1.33\).
We want to solve for \(x\). Rearranging the formula gives \(x=\mu+z\sigma\).
Substitute the values: \(x = 100+1.33\times15\).
Calculate \(1.33\times15 = 19.95\).
Then \(x=100 + 19.95=119.95\).

Answer:

\(120\)