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The image you provided contains two graphs related to the normal distribution. The first graph displays a normal distribution with a mean (\(\mu = 2\)) and a standard deviation (\(\sigma = 2\)), and the shaded region represents the probability of obtaining a value between -1 and 4.

The task is to shade the corresponding region under the **standard normal curve**, which has a mean of \(\mu = 0\) and a standard deviation of \(\sigma = 1\). To do this, you need to convert the boundaries \(-1\) and \(4\) into the standard normal distribution (z-scores) using the formula:

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

For \(x = -1\):
\[
z = \frac{-1 - 2}{2} = \frac{-3}{2} = -1.5
\]

For \(x = 4\):
\[
z = \frac{4 - 2}{2} = \frac{2}{2} = 1
\]

Thus, the corresponding region under the standard normal curve is between \(z = -1.5\) and \(z = 1\). This is the area that should be shaded in the lower graph.

Would you like more details or further clarification on this? Here are some related questions you might find useful:

1. How do we calculate the probability for this shaded region under the standard normal curve?
2. What is the general process for converting any normal distribution into the standard normal form?
3. How does the z-score help in comparing different normal distributions?
4. What is the significance of the mean and standard deviation in a normal distribution?
5. How do we use the standard normal table to find probabilities for specific z-scores?

**Tip:** When converting between different normal distributions, always standardize using the z-score formula to map values to the standard normal distribution.

Shade the corresponding region under the standard normal curve, given a normal distribution with mean μ = 2 and standard deviation σ = 2, where the shaded region represents the probability of obtaining a value between -1 and 4.

Learn how to shade the region under the standard normal curve by converting a given normal distribution (mean μ = 2, standard deviation σ = 2) to its z-scores. The problem involves calculating z-scores for the range between -1 and 4.

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