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.)

Step 1 ：The problem is asking for the area under the curve of a normal distribution, which represents the probability of a score falling within a certain range. The mean (\(\mu\)) is 100 and the standard deviation (\(\sigma\)) is 15.

Step 2 ：First, we need to calculate the z-scores for the lower and upper bounds of the range. The z-score is a measure of how many standard deviations an element is from the mean. The formula for the z-score is \(z = \frac{x - \mu}{\sigma}\).

Step 3 ：Let's calculate the z-scores for the lower bound (85) and the upper bound (115). For the lower bound, \(z_1 = \frac{85 - 100}{15} = -1.0\). For the upper bound, \(z_2 = \frac{115 - 100}{15} = 1.0\).

Step 4 ：The area under the curve of a normal distribution between two z-scores is given by the cumulative distribution function (CDF) for the normal distribution. The CDF gives the probability that a random variable is less than or equal to a certain value.

Step 5 ：Using the CDF, we can calculate the area under the curve between the two z-scores. The area is approximately 0.6827, which means there is a 68.27% chance that a randomly selected score will fall within this range.

Step 6 ：\(\boxed{\text{Final Answer: The area of the shaded region is approximately 0.6827.}}\)