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
86
The area of the shaded region is (Round to four decimal places as needed)
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Answer 1

Using the normal distribution, it is found that the area of the shaded region is of 0.8238.

Normal Probability Distribution

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

• It measures how many standard deviations the measure is from the mean.

• After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

• The mean is of $\mu = 100$.

• The standard deviation is of $\sigma = 15$.

• The area of the shaded region is 1 subtracted by the p-value of Z when X = 86.

Hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{86 - 100}{15}$

$Z = -0.93$

$Z = -0.93$ has a p-value of 0.1762.

1 - 0.1762 = 0.8238.

The area of the shaded region is of 0.8238.

More can be learned about the normal distribution at https://brainly.com/question/24663213