Question

find the area of the shaded region. 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 area of the shaded region is (round to four decimal places as needed.)

Explanation:

Step1: Standardize the value

First, we need to know the boundary value of the shaded - region. Let's assume the boundary value of the shaded region is \(x\). The z - score is calculated using the formula \(z=\frac{x - \mu}{\sigma}\), where \(\mu = 100\) (mean) and \(\sigma=15\) (standard deviation). Since the problem doesn't give the \(x\) value, if we assume we want to find the area to the right of a value \(x\), say \(x = 110\), then \(z=\frac{110 - 100}{15}=\frac{10}{15}\approx0.67\).

Step2: Use the standard normal table

The standard normal table gives the area to the left of a z - score. The total area under the standard - normal curve is 1. If \(z = 0.67\), from the standard normal table, the area to the left of \(z = 0.67\) is approximately \(0.7486\).
The area to the right of \(z = 0.67\) is \(1-0.7486 = 0.2514\).

Answer:

0.2514 (assuming the boundary value \(x = 110\). If a different boundary value is given, the steps are the same but the z - score calculation will change accordingly)