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This quiz involves finding areas under the standard normal curve based on specified z-scores. I'll walk through each question step-by-step:

### 1. Find the area under the normal curve below (to the left of) \( z = 1.25 \).
- You are asked to find the area to the left of \( z = 1.25 \). Using a standard normal distribution table or a calculator:
  \[
  P(Z < 1.25) \approx 0.8944
  \]
  So, the area is approximately 0.8944 or 89.44%.

### 2. Find the area under the normal curve above (to the right of) \( z = 2.06 \).
- To find the area to the right of \( z = 2.06 \):
  \[
  P(Z > 2.06) = 1 - P(Z < 2.06)
  \]
  Using a normal distribution table:
  \[
  P(Z < 2.06) \approx 0.9803
  \]
  So:
  \[
  P(Z > 2.06) = 1 - 0.9803 = 0.0197
  \]
  The area is approximately 0.0197 or 1.97%.

### 3. Find the area under the normal curve between \( z = 1.25 \) and \( z = 2.21 \).
- To find the area between two z-scores:
  \[
  P(1.25 < Z < 2.21) = P(Z < 2.21) - P(Z < 1.25)
  \]
  From the table:
  \[
  P(Z < 2.21) \approx 0.9864, \quad P(Z < 1.25) \approx 0.8944
  \]
  So:
  \[
  P(1.25 < Z < 2.21) = 0.9864 - 0.8944 = 0.0920
  \]
  The area is approximately 0.0920 or 9.20%.

### 4. Find the area under the normal curve between \( z = -1.73 \) and \( z = 0.96 \).
- To find the area between these two z-scores:
  \[
  P(-1.73 < Z < 0.96) = P(Z < 0.96) - P(Z < -1.73)
  \]
  From the table:
  \[
  P(Z < 0.96) \approx 0.8315, \quad P(Z < -1.73) \approx 0.0418
  \]
  So:
  \[
  P(-1.73 < Z < 0.96) = 0.8315 - 0.0418 = 0.7897
  \]
  The area is approximately 0.7897 or 78.97%.

Would you like further clarification or details on any of these questions?

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Here are five related questions to deepen your understanding:

1. How do you calculate the area for \( z \)-values greater than a given \( z \)?
2. What is the area under the curve between \( z = -1 \) and \( z = 1 \)?
3. How does the area under the normal curve change as \( z \)-values increase?
4. What is the total area under the normal distribution curve?
5. How do you interpret the area under the curve in a real-world context?

**Tip:** When working with normal distribution tables, remember that they usually provide the area to the left of the z-score. For right-tail areas, you need to subtract this value from 1.

Find areas under the normal curve for given z-scores.

This problem covers how to find areas under the normal curve for various z-scores. Concepts include finding the area to the left, to the right, and between two z-scores using the standard normal distribution table.

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