https://file.aiquickdraw.com/mathbot/file/1728884266347bgyn1ple.jpg

The image shows a problem involving a **normal distribution** with mean \(\mu = -2\) and standard deviation \(\sigma = 3\). The shaded region represents the probability of obtaining a value greater than 1. You're asked to shade the corresponding region under the **standard normal curve** (a normal distribution with \(\mu = 0\) and \(\sigma = 1\)).

### Steps to approach this:

1. **Standardize the value**: To find the corresponding region under the standard normal curve, we need to convert the value \(x = 1\) to a **z-score** using the formula:
   \[
   z = \frac{x - \mu}{\sigma}
   \]
   For this problem:
   \[
   z = \frac{1 - (-2)}{3} = \frac{1 + 2}{3} = \frac{3}{3} = 1
   \]
   So, the z-score corresponding to \(x = 1\) in this distribution is \(z = 1\).

2. **Shade the region**: In the standard normal distribution, you would shade the area to the right of \(z = 1\). This represents the probability of obtaining a value greater than 1 in the standard normal curve.

In the bottom graph, you need to shade the area from \(z = 1\) to the right.

Would you like further details on how to calculate or interpret this probability?

### Related questions:
1. What is the total area under a standard normal curve?
2. How do we interpret z-scores in real-world problems?
3. How can we use z-tables to find probabilities for normal distributions?
4. What is the probability of obtaining a value greater than 1 in this specific distribution?
5. How can you use the empirical rule to estimate probabilities in normal distributions?

### Tip:
Remember that the total area under any normal distribution curve equals 1, representing the total probability.

Below is a graph of a normal distribution with mean μ = -2 and standard deviation σ = 3. The shaded region represents the probability of obtaining a value from this distribution that is greater than 1. Shade the corresponding region under the standard normal curve below.

Learn how to shade the region under the standard normal curve corresponding to a normal distribution with mean μ = -2 and standard deviation σ = 3. This problem involves calculating z-scores and understanding the properties of normal distributions, suitable for Grades 10-12 or College-level statistics.

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