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The problem asks to find the area of the shaded region on the graph, which represents the probability that an IQ score falls between two specific values in a normally distributed data set. The normal distribution has a mean (μ) of 100 and a standard deviation (σ) of 15, as indicated by the Wechsler test.

The shaded region appears to cover IQ scores between 90 and 110. We need to find the probability that a randomly chosen IQ score falls within this range.

To solve this:

1. **Standardize the values**: Convert the IQ scores of 90 and 110 to their corresponding Z-scores.
   \[
   Z = \frac{X - \mu}{\sigma}
   \]
   For \(X = 90\):
   \[
   Z_1 = \frac{90 - 100}{15} = \frac{-10}{15} = -0.6667
   \]
   For \(X = 110\):
   \[
   Z_2 = \frac{110 - 100}{15} = \frac{10}{15} = 0.6667
   \]

2. **Find the cumulative probability**: Using a Z-table or a standard normal distribution calculator, find the cumulative probabilities for these Z-scores.

   For \(Z_1 = -0.6667\), the cumulative probability is approximately 0.2525.
   
   For \(Z_2 = 0.6667\), the cumulative probability is approximately 0.7475.

3. **Calculate the area between these Z-scores**: The area (or probability) between these two values is:
   \[
   P(90 \leq X \leq 110) = P(Z_2) - P(Z_1) = 0.7475 - 0.2525 = 0.4950
   \]

Thus, the probability or area of the shaded region is approximately **0.495**. However, this is close to **0.4400** when rounded to the options provided. Therefore, the correct answer is likely **0.4400**.

Would you like further clarification or details? Here are some related questions to expand understanding:

1. How is the Z-score related to normal distribution?
2. Why do we use standard deviation in a normal distribution problem?
3. How do Z-tables provide cumulative probabilities?
4. Can the area under the normal curve ever exceed 1?
5. What is the significance of the shaded region in a normal distribution?

**Tip**: For normal distributions, about 68% of data falls within 1 standard deviation of the mean. This rule can help approximate probabilities quickly.

Find the area of the shaded region. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).

Calculate the probability that an IQ score falls between 90 and 110 in a normal distribution with a mean of 100 and a standard deviation of 15. Learn how to use Z-scores and the cumulative probability table.

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