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The problem provided involves a normal distribution, with a mean \( \mu = 43 \) minutes and a standard deviation \( \sigma = 7 \) minutes. Let's address each part of the problem step-by-step:

### 1. Fill in the indicated boxes on the bell curve:
This normal distribution is centered around \( \mu = 43 \). Since the scale on the horizontal axis is based on standard deviations, we can fill in the boxes using multiples of \( \sigma \).

- \( \mu - 30 = \mu - 3\sigma = 43 - 3(7) = 43 - 21 = 22 \)
- \( \mu - 20 = \mu - 2\sigma = 43 - 2(7) = 43 - 14 = 29 \)
- \( \mu - 10 = \mu - \sigma = 43 - 7 = 36 \)
- \( \mu = 43 \)
- \( \mu + 10 = \mu + \sigma = 43 + 7 = 50 \)
- \( \mu + 20 = \mu + 2\sigma = 43 + 14 = 57 \)
- \( \mu + 30 = \mu + 3\sigma = 43 + 21 = 64 \)

So, the boxes should be filled in as:
- 22, 29, 36, 43, 50, 57, 64.

### 2. Using the Empirical Rule to complete the following statements:
The Empirical Rule states the following:
- 68% of the data falls within 1 standard deviation of the mean.
- 95% of the data falls within 2 standard deviations of the mean.
- 99.7% of the data falls within 3 standard deviations of the mean.

Now let's apply this to the statements:
1. **68% of testing times were between \( \mu - \sigma \) and \( \mu + \sigma \):**
   - \( 43 - 7 = 36 \) and \( 43 + 7 = 50 \).
   - So, **68% of testing times were between 36 minutes and 50 minutes.**

2. **95% of the testing times were between \( \mu - 2\sigma \) and \( \mu + 2\sigma \):**
   - \( 43 - 14 = 29 \) and \( 43 + 14 = 57 \).
   - So, **95% of the testing times were between 29 minutes and 57 minutes**.

### Summary:
- Boxes on the graph: 22, 29, 36, 43, 50, 57, 64.
- 68% of testing times are between 36 and 50 minutes.
- 95% of testing times are between 29 and 57 minutes.

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### Related Questions:
1. How would the graph change if the mean was higher, such as \( \mu = 50 \)?
2. What percentage of the data falls within 2.5 standard deviations of the mean?
3. How can we calculate the z-score for a time of 55 minutes?
4. How does changing the standard deviation affect the shape of the bell curve?
5. Can we use the Empirical Rule to estimate percentages outside 3 standard deviations?

### Tip:
Always remember the Empirical Rule (68-95-99.7) for quick estimates in normal distributions!

The time to complete an exam is approximately Normal with a mean μ = 43 minutes and a standard deviation σ = 7 minutes. The bell curve represents the distribution for testing times. Using the Empirical Rule, fill in the indicated boxes and complete the statements.

Solve a normal distribution problem where the time to complete an exam follows a normal distribution with mean μ = 43 and standard deviation σ = 7. Learn how to apply the Empirical Rule to fill in distribution values and determine the percentage of data within 1 or 2 standard deviations of the mean.

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