Find the area to the between z = -1.20 and z = -0.87

To find the area between the \( z \)-scores \( z = -1.20 \) and \( z = -0.87 \), we need to use the standard normal distribution table or a calculator that provides the cumulative probabilities (or areas) under the standard normal curve.

### Step-by-Step Calculation:

1. **Find the cumulative probability for \( z = -1.20 \)**:
   - Using the standard normal distribution table or a calculator, the cumulative probability for \( z = -1.20 \) is approximately \( 0.1151 \).

2. **Find the cumulative probability for \( z = -0.87 \)**:
   - The cumulative probability for \( z = -0.87 \) is approximately \( 0.1922 \).

3. **Subtract the two probabilities to get the area between the two \( z \)-scores**:
   \[
   \text{Area} = P(z = -0.87) - P(z = -1.20) = 0.1922 - 0.1151 = 0.0771
   \]

Thus, the area between \( z = -1.20 \) and \( z = -0.87 \) is approximately **0.0771**.

Would you like more details or have any questions?

Here are five related questions to explore further:
1. How do you interpret areas under the standard normal curve in practical applications?
2. What is the total area under the standard normal curve?
3. How do you find the area between two positive \( z \)-scores?
4. How can you calculate areas beyond a given \( z \)-score, such as \( z > 2 \)?
5. What is the meaning of a cumulative probability in a standard normal distribution?

**Tip:** The area under the standard normal curve between any two points represents the probability that a value lies between those two points.

Discover how to calculate the area between z-scores -1.20 and -0.87 using the standard normal distribution. This guide includes key probability concepts, step-by-step calculations, and insights into cumulative probabilities. Suitable for high school students in Grades 10-12.

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