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.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 88\), \(\mu=100\), and \(\sigma = 15\).

$$z=\frac{88 - 100}{15}=\frac{-12}{15}=- 0.8$$

Step2: Find the area using the standard normal table

We want to find \(P(X>88)\), which is equivalent to \(P(Z>-0.8)\).
Since \(P(Z > - 0.8)=1 - P(Z\leqslant-0.8)\).
Looking up the value of \(P(Z\leqslant-0.8)\) in the standard - normal table (z - table), we get \(P(Z\leqslant-0.8)=0.2119\).
Then \(P(Z>-0.8)=1 - 0.2119 = 0.7881\)

Answer:

\(0.7881\)