To shade the corresponding region on the standard normal curve, we need to first convert the boundaries of the shaded area on the original curve (from 7 to 10) to the standard normal distribution using the $Z$-score formula:

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

Given Information

• Mean ($\mu$) = 4
• Standard deviation ($\sigma$) = 3
• We want to find the $Z$-scores for $X = 7$ and $X = 10$.

Step 1: Calculate the $Z$-scores

1. For $X = 7$: $Z = \frac{7 - 4}{3} = \frac{3}{3} = 1$

2. For $X = 10$: $Z = \frac{10 - 4}{3} = \frac{6}{3} = 2$

Step 2: Shade the Corresponding Region

On the standard normal curve, shade the area between $Z = 1$ and $Z = 2$. This shaded region represents the probability of obtaining a value between 7 and 10 in the original distribution.

Would you like further assistance with interpreting this or have additional questions?

Here are some related questions for deeper understanding:

1. How is the area under the normal curve related to probability?
2. What are some typical uses of the $Z$-score in statistics?
3. Why is the standard normal distribution centered at zero?
4. How would you calculate probabilities for values below the mean?
5. What are the applications of normal distribution in real-life scenarios?

Tip: Converting values to $Z$-scores standardizes them, allowing you to compare scores from different normal distributions on the same scale.