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

Since the area to the left of \(x\) is \(0.75\). Looking up in the standard normal distribution table (z - table), the \(z\) - score corresponding to an area of \(0.75\) is approximately \(z = 0.67\).

Step2: 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 want to solve for \(x\), so we can rewrite the formula as \(x=\mu + z\sigma\).
Substitute \(\mu = 100\), \(z = 0.67\), and \(\sigma = 15\) into the formula:
\(x=100+0.67\times15\)
\(x = 100+10.05\)
\(x=110.05\)

Answer:

\(110\)