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.

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Answer 1

Solution:

We are given:

\(\mu=100, \sigma=15\)

We have to find the area of the given shaded region.

\(P(102

First, we will use the z score formula to standardize the given scores.

\(=P\left(\frac{102-100}{15}

\(=P(0.1333

\(=P(z<1.8667)-P(z<0.1333)\)

Now using the standard normal table, we have:

\(=0.4160\)

Therefore, the area of the shaded region is \(0.4160\)