According to National Testing data, college math class testing times are Normally distributed with a mean of 39 minutes and standard deviation 5 minutes.

The bell curve below represents the probability distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. Fill in the three indicated boxes.



To fill in the three indicated boxes on the bell curve, we need to understand how the normal distribution works in terms of the standard deviation (SD) from the mean. The mean, in this case, is 39 minutes, and the standard deviation is 5 minutes.

In a normal distribution:

- **68%** of the data falls within **±1 standard deviation** from the mean.
- **95%** of the data falls within **±2 standard deviations** from the mean.
- **99.7%** of the data falls within **±3 standard deviations** from the mean.

Now let's fill in the boxes:

1. **At the mean (center of the curve):** This is simply the mean value, which is 39 minutes.

2. **One standard deviation to the right of the mean:** This would be the mean plus one standard deviation:
   \[
   39 + 5 = 44 \text{ minutes}
   \]

3. **Two standard deviations to the right of the mean:** This would be the mean plus two standard deviations:
   \[
   39 + 2(5) = 39 + 10 = 49 \text{ minutes}
   \]

Thus, the three indicated boxes on the bell curve should contain:
- Mean = 39 minutes (center)
- 44 minutes (1 SD to the right)
- 49 minutes (2 SDs to the right)

Would you like any additional details or have any questions about this? 

Here are 5 questions related to this topic:
1. What percentage of students take between 34 and 44 minutes to complete the test?
2. How many students finish in less than 34 minutes if there are 200 students?
3. What are the testing times corresponding to 1 and 2 standard deviations to the left of the mean?
4. How do you calculate probabilities for times beyond 3 standard deviations from the mean?
5. How would this change if the standard deviation were 6 minutes instead of 5?

**Tip:** When solving problems related to the normal distribution, always keep track of the relationship between the mean, standard deviation, and z-scores!

According to National Testing data, college math class testing times are Normally distributed with a mean of 39 minutes and standard deviation 5 minutes. The bell curve below represents the probability distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. Fill in the three indicated boxes.

Explore the normal distribution for college math class testing times, with a mean of 39 minutes and a standard deviation of 5 minutes. This problem uses the 68-95-99.7 rule to fill in the indicated values on a bell curve. Suitable for Grades 10-12.

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