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.

To find the area of the shaded region under the curve, which represents the probability corresponding to certain IQ scores, we need more information about the range of IQ scores that define the shaded area. Typically, problems like this involve shading part of a normal distribution between two IQ scores, and we would calculate the area (probability) within that range.

However, without the graph, we can still follow these steps if you provide the IQ score range or cutoff values for the shaded region. The general approach is as follows:

1. **Standardize the IQ scores**: 
   Convert the given IQ scores to **z-scores** using the formula:
   \[
   z = \frac{x - \mu}{\sigma}
   \]
   where:
   - \(x\) is the IQ score,
   - \(\mu = 100\) (the mean IQ),
   - \(\sigma = 15\) (the standard deviation).

2. **Look up the z-scores**:
   Use a standard normal distribution table or calculator to find the probabilities corresponding to the z-scores.

3. **Subtract the cumulative probabilities**:
   To find the area of the shaded region between two z-scores, subtract the cumulative probability of the lower z-score from the cumulative probability of the higher z-score.

If you can upload the image or specify the range of IQ scores for the shaded area, I can give you the precise answer.

Do you want details on these steps? Here are 5 related questions:

1. What is a z-score, and how is it used in normal distributions?
2. How do you interpret areas under a normal distribution curve?
3. What does a standard normal distribution table represent?
4. How can IQ scores be used to determine probabilities?
5. How does changing the mean or standard deviation affect the distribution?

**Tip**: When working with normal distributions, sketching the curve and shading the relevant area often helps visualize the problem better.

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.

Learn how to calculate the area of the shaded region in a normal distribution graph of IQ scores, given a mean of 100 and a standard deviation of 15. This problem covers key concepts like z-scores, probability, and normal distribution. Suitable for students in Grades 10-12.

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