To solve this problem using the 68-95-99.7 Rule, we need to understand what the rule tells us about the distribution of data:

• 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.

Step 1: Find the range of values in terms of standard deviations from the mean.

Given:

• Mean ($\mu$) = 39
• Standard deviation ($\sigma$) = 11

We need to find the percentage of daily phone calls between 17 and 61.

• Lower bound: $17$
• Upper bound: $61$

Step 2: Calculate how many standard deviations these values are from the mean.

For the lower bound (17):

$\text{z}_\text{lower} = \frac{17 - 39}{11} = \frac{-22}{11} = -2$

For the upper bound (61):

$\text{z}_\text{upper} = \frac{61 - 39}{11} = \frac{22}{11} = 2$

So, 17 is 2 standard deviations below the mean, and 61 is 2 standard deviations above the mean.

Step 3: Apply the 68-95-99.7 Rule.

• 68% of the data is between 1 standard deviation below and above the mean (between 28 and 50).
• 95% of the data is between 2 standard deviations below and above the mean (between 17 and 61).

Therefore, 95% of the daily phone calls fall between 17 and 61.

Final Answer:

The approximate percentage of daily phone calls numbering between 17 and 61 is 95%.

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Would you like more details or clarification on any part of this? Here are some follow-up questions that could expand on this topic:

1. How can you apply the 68-95-99.7 Rule to a non-bell-shaped distribution?
2. What does it mean if a data set does not follow a normal distribution?
3. How would you calculate the probability of a number of calls outside this range?
4. What is the significance of using standard deviations in this kind of analysis?
5. How does the central limit theorem relate to the 68-95-99.7 Rule?

Tip: Always visualize the data in terms of standard deviations from the mean to quickly assess probabilities in a normal distribution.