Find the area under the standard normal distribution curve between z=−1 and z=−2
. Refer to the table of values Area Under the Standard Normal Distribution as needed.
The area between z=−1 and z=−2 is .





To find the area under the standard normal distribution curve between \( z = -1 \) and \( z = -2 \), we need to look at the cumulative distribution function (CDF) values for these two \( z \)-scores. This can be done by consulting the **Z-table**, which gives the area under the curve from \( z = -\infty \) to a particular \( z \)-value.

Steps to find the area:

1. **Find the cumulative area for \( z = -1 \)**:
   - From the Z-table, the cumulative area for \( z = -1.00 \) is **0.1587**.

2. **Find the cumulative area for \( z = -2 \)**:
   - From the Z-table, the cumulative area for \( z = -2.00 \) is **0.0228**.

3. **Calculate the area between \( z = -1 \) and \( z = -2 \)**:
   - The area between these two \( z \)-values is the difference between the cumulative areas:
   \[
   \text{Area} = 0.1587 - 0.0228 = 0.1359
   \]

Thus, the area under the standard normal distribution curve between \( z = -1 \) and \( z = -2 \) is **0.1359**.

Would you like more details, or do you have any questions?

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Here are 5 related questions for practice:
1. What is the area under the standard normal curve for \( z \)-values between 0 and 1?
2. How do you calculate the area under the curve for negative \( z \)-values using the Z-table?
3. What is the total area under the standard normal distribution curve?
4. How would you find the area between \( z = -1.5 \) and \( z = 1.5 \)?
5. Can you explain why the standard normal distribution curve is symmetric?

**Tip**: Remember that the total area under the entire standard normal curve is always 1, representing 100% of the data under the curve.

Find the area under the standard normal distribution curve between z = −1 and z = −2. Refer to the table of values Area Under the Standard Normal Distribution as needed. The area between z = −1 and z = −2 is .

Learn how to calculate the area under the standard normal distribution curve between z = -1 and z = -2 using the Z-table. This step-by-step guide provides a solution for finding the cumulative distribution function values and their difference. Suitable for Grades 11-12 statistics students.

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