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 corresponding to the area

We know that the total area under the normal - curve is 1. If the area to the left of the value \(x\) is \(0.8\), we use the standard normal distribution table (z - table). Looking up the value \(0.8\) in the body of the standard normal distribution table, the corresponding z - score \(z\) is approximately \(0.84\).

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 \(\mu = 100\), \(z = 0.84\), and \(\sigma = 15\) into the formula: \(x=100 + 0.84\times15\).

Step3: Calculate the value of \(x\)

First, calculate \(0.84\times15=12.6\). Then, \(x=100 + 12.6=112.6\).
Rounding to the nearest whole number, \(x = 113\).

Answer:

113