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The problem involves a normal distribution with a mean (\(\mu\)) of 3 and a standard deviation (\(\sigma\)) of 4. The task is to shade the region under the standard normal curve that corresponds to the probability of obtaining a value greater than 9.

### Steps to solve:

1. **Standardize the value**: First, we need to convert the value 9 from the given normal distribution to a standard normal distribution (mean 0, standard deviation 1) by using the Z-score formula:
   
   \[
   Z = \frac{X - \mu}{\sigma}
   \]
   
   Where:
   - \(X = 9\) (the value we are interested in)
   - \(\mu = 3\)
   - \(\sigma = 4\)

   Substituting the values:

   \[
   Z = \frac{9 - 3}{4} = \frac{6}{4} = 1.5
   \]

2. **Shade the region corresponding to \( Z > 1.5 \)**: On a standard normal curve, \( Z = 1.5 \) is to the right of the mean (0). The region we need to shade is the area under the curve to the right of \( Z = 1.5 \).

In the bottom graph, which is a standard normal curve, you should shade the area starting from \( Z = 1.5 \) and extending to the right (the tail).

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Would you like more details on standard normal distribution or how to calculate probabilities using the Z-table?

Here are some related questions:
1. How do you calculate the area under a normal curve?
2. What is the probability of \( Z > 1.5 \) using the Z-table?
3. What is the significance of the standard normal distribution in statistics?
4. How does changing the mean and standard deviation affect the shape of the normal distribution?
5. What does the area under the curve represent in a probability distribution?

**Tip**: When converting between a normal distribution and a standard normal distribution, always use the Z-score formula.

Below is a graph of a normal distribution with mean μ = 3 and standard deviation σ = 4. The shaded region represents the probability of obtaining a value from this distribution that is greater than 9. Shade the corresponding region under the standard normal curve below.

Learn how to solve a standard normal distribution problem where a value greater than 9 is given from a normal distribution with mean 3 and standard deviation 4. Follow step-by-step instructions to convert the value using the Z-score formula and shade the appropriate region under the standard normal curve.

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