. Find the area under the standard normal distribution curve between z = 0 and z = 2.16. A) 2.1600 B) 0.9846 C) 0.4846 D) 0.3708

To find the area under the standard normal distribution curve between \( z = 0 \) and \( z = 2.16 \), we need to use the standard normal distribution table (or Z-table) or a calculator to find the cumulative probability for \( z = 2.16 \), then subtract the cumulative probability for \( z = 0 \).

1. **Step 1: Find the cumulative probability for \( z = 2.16 \)**  
From the Z-table, the cumulative probability for \( z = 2.16 \) is approximately 0.9846.

2. **Step 2: Find the cumulative probability for \( z = 0 \)**  
The cumulative probability for \( z = 0 \) is exactly 0.5 (as it is the center of the distribution).

3. **Step 3: Subtract the cumulative probability at \( z = 0 \) from that at \( z = 2.16 \):**
\[
\text{Area} = 0.9846 - 0.5 = 0.4846
\]

Thus, the area under the curve between \( z = 0 \) and \( z = 2.16 \) is **0.4846**.

The correct answer is **C) 0.4846**.

Would you like further details or have any questions?

Here are some related questions:
1. What is the total area under the standard normal curve?
2. How is the cumulative probability interpreted in a normal distribution?
3. What is the area between \( z = -1 \) and \( z = 1 \)?
4. How would you find the area under the curve for negative Z-scores?
5. How do you calculate Z-scores for non-standard normal distributions?

**Tip:** The total area under a standard normal distribution curve is always 1, as it represents a probability distribution.

Find the area under the standard normal distribution curve between z = 0 and z = 2.16. A) 2.1600 B) 0.9846 C) 0.4846 D) 0.3708

Learn how to find the area under the standard normal distribution curve between z = 0 and z = 2.16. This step-by-step guide covers concepts such as Z-scores, cumulative probability, and how to use Z-tables. Suitable for high school students in Grades 10-12.

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