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. click to view page 1 of the table. click to view page 2 of the table. 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 \(z=\frac{x-\mu}{\sigma}\), where \(x = 75\), \(\mu=100\), and \(\sigma = 15\).

$$z=\frac{75 - 100}{15}=\frac{-25}{15}\approx - 1.67$$

Step2: Find the area using the standard normal table

We want to find \(P(X>75)\), which is equivalent to \(P(Z>-1.67)\).
Since \(P(Z > z)=1 - P(Z\leq z)\), and from the standard - normal table \(P(Z\leq - 1.67)=0.0475\)

$$P(Z>-1.67)=1 - 0.0475 = 0.9525$$

Answer:

\(0.9525\)