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 right of the value \(x\) is \(0.1826\). So the area to the left of \(x\) is \(A = 1 - 0.1826=0.8174\). Looking up this area in the standard - normal distribution table (z - table), the corresponding z - score \(z\) is approximately \(0.91\).

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 \(z = 0.91\). We want to solve for \(x\). Rearranging the formula gives \(x=\mu+z\sigma\).
Substitute the values: \(x = 100+0.91\times15\).

Step3: Calculate the value of \(x\)

First, calculate \(0.91\times15 = 13.65\). Then \(x=100 + 13.65=113.65\).
Rounding to the nearest whole number, \(x\approx114\).

Answer:

114