https://file.aiquickdraw.com/mathbot/file/1729490992688fdpatgrz.jpg

The problem you are working on involves normal distribution and requires shading the corresponding region under the standard normal curve, based on the given data.

### Given:
- The original normal distribution has a mean (\(\mu\)) of 4 and a standard deviation (\(\sigma\)) of 2.
- The problem asks for the probability of obtaining a value between 3 and 6.

### Step 1: Convert to Z-scores
You need to convert the values 3 and 6 from the original distribution to the standard normal distribution (with mean 0 and standard deviation 1). The formula for converting a raw score to a Z-score is:

\[
Z = \frac{X - \mu}{\sigma}
\]

Where \(X\) is the value from the original distribution.

For \(X = 3\):

\[
Z_1 = \frac{3 - 4}{2} = \frac{-1}{2} = -0.5
\]

For \(X = 6\):

\[
Z_2 = \frac{6 - 4}{2} = \frac{2}{2} = 1
\]

### Step 2: Shade the Corresponding Region
The standard normal curve should have a shaded region between \(Z = -0.5\) and \(Z = 1\). Based on the graph below, you should mark the area between these Z-values.

- The left endpoint of the shaded region corresponds to \(Z = -0.5\).
- The right endpoint of the shaded region corresponds to \(Z = 1\).

### Correction for Your Attempt:
It seems the original attempt did not correctly shade this area. You need to select the region between \(Z = -0.5\) and \(Z = 1\) on the standard normal curve, which reflects the transformation from the original normal distribution.

Would you like further details on how to calculate probabilities or interpret the Z-scores? 

Here are some additional questions to further explore this topic:

1. How do you calculate probabilities for a normal distribution using Z-scores?
2. What is the importance of the standard normal curve in statistics?
3. How can you use a Z-table or technology to find the area under a normal curve?
4. Why do we use the standard normal distribution to compare different datasets?
5. How does the shape of the normal curve change with different standard deviations?

**Tip:** Always check the Z-scores and ensure correct interpretation before shading the area on the standard normal curve.

Below is a graph of a normal distribution with mean μ=4 and standard deviation σ=2. The shaded region represents the probability of obtaining a value from this distribution that is between 3 and 6. Shade the corresponding region under the standard normal curve.

Solve a normal distribution problem where the mean is 4 and standard deviation is 2. Learn how to convert raw scores into Z-scores and shade the correct region on the standard normal curve. This problem includes calculating Z-scores for values between 3 and 6 and shading the appropriate area.

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