Find the area under the normal distributing curve between Z=-0.81 and Z= 0.56

To find the area under the normal distribution curve between \( Z = -0.81 \) and \( Z = 0.56 \), we can use the standard normal distribution table or a calculator that provides the cumulative distribution function (CDF) for the standard normal distribution.

Here are the steps:

1. **Find the CDF for \( Z = 0.56 \):**
   - The CDF value for \( Z = 0.56 \) is approximately 0.7123.

2. **Find the CDF for \( Z = -0.81 \):**
   - The CDF value for \( Z = -0.81 \) is approximately 0.2090.

3. **Calculate the area between \( Z = -0.81 \) and \( Z = 0.56 \):**
   - Subtract the CDF value of \( Z = -0.81 \) from the CDF value of \( Z = 0.56 \):
   \[
   \text{Area} = 0.7123 - 0.2090 = 0.5033
   \]

The area under the normal distribution curve between \( Z = -0.81 \) and \( Z = 0.56 \) is **0.5033**.

Would you like more details or have any questions?

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Here are 8 related questions you might find interesting:

1. What is the total area under the standard normal distribution curve?
2. How do you find the Z-score for a given value in a normal distribution?
3. What is the significance of the area under the curve in a normal distribution?
4. How do you calculate the area to the left of a given Z-score?
5. How do you calculate the area to the right of a given Z-score?
6. What does it mean if the Z-score is negative?
7. How do you interpret the Z-score in terms of probability?
8. How can you use a Z-table to find areas under the curve?

**Tip:** Always check if your Z-scores are within the standard normal distribution range before proceeding with calculations!

Learn how to find the area under the normal distribution curve between Z=-0.81 and Z=0.56 using the cumulative distribution function (CDF) and standard normal distribution table. Step-by-step solution provided.

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