https://file.aiquickdraw.com/mathbot/file/1728245354492xf6kcz34.jpg

The given image shows a normal distribution with a mean (\( \mu \)) of 4 and a standard deviation (\( \sigma \)) of 3. The shaded region represents the probability that a value from this distribution is greater than 2.5. 

To shade the corresponding region under the standard normal curve, we need to convert the value 2.5 into a standard normal variable using the z-score formula:

\[
z = \frac{x - \mu}{\sigma}
\]

Given:
- \( x = 2.5 \)
- \( \mu = 4 \)
- \( \sigma = 3 \)

The z-score becomes:

\[
z = \frac{2.5 - 4}{3} = \frac{-1.5}{3} = -0.5
\]

So, under the standard normal curve (mean 0, standard deviation 1), the z-score corresponding to \( x = 2.5 \) is \( z = -0.5 \). The shaded region in the second plot should represent the area greater than \( z = -0.5 \), meaning from \( z = -0.5 \) to infinity.

Let me know if you'd like further details or if you want me to mark the region in any specific way. Here are some related questions:

1. What is the significance of a z-score in a normal distribution?
2. How would the z-score change if the mean or standard deviation was different?
3. How do you calculate probabilities using the z-table for areas under the curve?
4. What does it mean if the z-score is positive versus negative?
5. Can you compute the probability from the z-score for this example?

**Tip**: Remember, the total area under a normal curve is always equal to 1, which corresponds to 100% probability.

Shade the corresponding region under the standard normal curve for a distribution with mean μ = 4, standard deviation σ = 3, where x > 2.5.

Learn how to shade the region of a normal distribution with a mean of 4 and standard deviation of 3, where the probability is for values greater than 2.5. This tutorial covers the use of z-scores and the normal distribution curve. Suitable for high school and college students.

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