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.