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: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\). Here, \(x = 100\), \(\mu=100\), and \(\sigma = 15\).

$$z=\frac{100 - 100}{15}=0$$

Step2: Find the area using the standard normal distribution table

The area to the left of \(z = 0\) in the standard normal distribution table is \(0.5\). Since the total area under the normal curve is \(1\), and we want the area to the right of \(z = 0\) (the shaded region), we use the formula \(A=1 - P(Z<z)\).

$$A = 1-0.5=0.5$$

Answer:

\(0.5000\)