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

We know that the area to the left of the value \(x\) is \(0.5 + 0.3949=0.8949\). Looking up this value in the standard normal distribution table (z - table), the corresponding z - score \(z\) is approximately \(1.25\).

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 \(z = 1.25\). We want to solve for \(x\). Rearranging the formula gives \(x=\mu+z\sigma\).
Substitute the values: \(x = 100+1.25\times15\).

Step3: Calculate \(x\)

First, calculate \(1.25\times15 = 18.75\). Then \(x=100 + 18.75=118.75\).

Answer:

119