This problem involves a normal distribution with a mean ($\mu$) of 56 minutes and a standard deviation ($\sigma$) of 3 minutes. In a normal distribution, values at specific intervals from the mean can be calculated by adding or subtracting multiples of the standard deviation.

The boxes represent values at increments of one standard deviation. Let's calculate these values:

1. Two standard deviations below the mean: $56 - 2 \times 3 = 56 - 6 = 50$

2. One standard deviation below the mean: $56 - 1 \times 3 = 56 - 3 = 53$

3. The mean: $56$

4. One standard deviation above the mean: $56 + 1 \times 3 = 56 + 3 = 59$

5. Two standard deviations above the mean: $56 + 2 \times 3 = 56 + 6 = 62$

Filling in the Boxes:

• The left-most box (two standard deviations below the mean): 50
• The middle-left box (one standard deviation below the mean): 53
• The middle-right box (one standard deviation above the mean): 59
• The right-most box (two standard deviations above the mean): 62

So, the boxes should be filled in with:

1. 50
2. 53
3. 59

Would you like more details or have any questions?

Related Questions

1. What percentage of data lies within one standard deviation of the mean in a normal distribution?
2. How do you calculate probabilities using the z-score in a normal distribution?
3. What is the probability of a test time being more than two standard deviations from the mean?
4. Why is the bell curve symmetric around the mean in a normal distribution?
5. How would the distribution change if the standard deviation increased?

Tip:

In a normal distribution, approximately 68% of data falls within one standard deviation, 95% within two, and 99.7% within three standard deviations of the mean.