The graph you've provided represents the normal distribution curve, often used in statistics to find probabilities or areas under the curve based on $Z$-scores. To find the area between $Z = 1.37$ and $Z = 2.55$, we'll use the standard normal table (Z-table) or a computational method. Here’s the process:

Step-by-Step Solution:

1. Identify the cumulative area for $Z = 1.37$: From the Z-table, the cumulative area up to $Z = 1.37$ is approximately 0.9147.

2. Identify the cumulative area for $Z = 2.55$: From the Z-table, the cumulative area up to $Z = 2.55$ is approximately 0.9946.

3. Find the area between $Z = 1.37$ and $Z = 2.55$: Subtract the cumulative area for $Z = 1.37$ from the cumulative area for $Z = 2.55$: $\text{Area} = 0.9946 - 0.9147 = 0.0799$

Final Answer:

The area between $Z = 1.37$ and $Z = 2.55$ is 0.0799.

Would you like further explanations on the process or how the Z-table works?

Related Questions:

1. How do you interpret the area under the normal curve in terms of probability?
2. What does a $Z$-score represent in a standard normal distribution?
3. How can technology (e.g., calculators or software) simplify these calculations?
4. How would the area change if the range of $Z$-scores were negative?
5. Can you explain how to find areas for a two-tailed test using the normal curve?

Tip:

When working with $Z$-scores, always verify whether you're looking for a one-tailed or two-tailed area and carefully read the Z-table for cumulative probabilities.