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We are asked to find two areas on the standard normal curve based on \( z \)-scores: 

1. The area **to the right of** \( z = 1.38 \).
2. The area **to the left of** \( z = 1.53 \).

We will use the values from the provided standard normal table.

### Step 1: Find the cumulative area for \( z = 1.38 \)
From the table:
- The row for \( z = 1.3 \) and the column for 0.08 gives \( P(z \leq 1.38) = 0.9162 \).

The area to the **right of \( z = 1.38 \)** is:
\[
P(z > 1.38) = 1 - P(z \leq 1.38) = 1 - 0.9162 = 0.0838.
\]

### Step 2: Find the cumulative area for \( z = 1.53 \)
From the table:
- The row for \( z = 1.5 \) and the column for 0.03 gives \( P(z \leq 1.53) = 0.9370 \).

The area to the **left of \( z = 1.53 \)** is:
\[
P(z \leq 1.53) = 0.9370.
\]

### Conclusion:
- The area to the right of \( z = 1.38 \) is **0.0838**.
- The area to the left of \( z = 1.53 \) is **0.9370**.

Would you like further explanation, or do you have any questions?

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Here are 5 related questions to consider:
1. What is the total area between \( z = 1.38 \) and \( z = 1.53 \)?
2. How do we interpret the area under the normal curve in practical terms?
3. What is the area to the right of \( z = 1.53 \)?
4. How does the area change as \( z \)-scores increase?
5. How would you calculate the area between two arbitrary \( z \)-scores using a table?

**Tip**: The total area under the standard normal curve is always 1 (representing 100% of the distribution).

Find the area to the right of the z-score 1.38 and to the left of the z-score 1.53 under the standard normal curve.

Learn how to find the area to the right of z = 1.38 and the area to the left of z = 1.53 using a standard normal table. This detailed solution covers statistical concepts and provides step-by-step calculations. Suitable for students in Grades 10-12 or introductory college statistics.

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