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 value \(x\) is \(0.7\). Looking up this area in the standard - normal distribution table (z - table), the z - score corresponding to an area of \(0.7\) is approximately \(z = 0.52\).

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 \(z\) is the z - score. We want to solve for \(x\). Rearranging the formula gives \(x=\mu + z\sigma\).
Substitute \(\mu = 100\), \(z = 0.52\), and \(\sigma = 15\) into the formula: \(x=100+0.52\times15\).

Step3: Calculate the value of \(x\)

First, calculate \(0.52\times15 = 7.8\). Then, \(x=100 + 7.8=107.8\). Rounding to the nearest whole number, \(x = 108\).

Answer:

108