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 right of \(x\) is \(0.55\), the area to the left of \(x\) is \(1 - 0.55=0.45\). Looking up \(0.45\) in the standard normal distribution table, the closest \(z\) - score is \(z=- 0.13\) (using linear interpolation or standard table values).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 100\), \(\sigma=15\), and \(z=-0.13\).
Substitute the values into the formula: \(-0.13=\frac{x - 100}{15}\).
Multiply both sides by \(15\): \(-0.13\times15=x - 100\).
\(-1.95=x - 100\).
Add \(100\) to both sides: \(x=100-1.95\).

Answer:

\(x = 98\)