The empirical rule, also known as the 68-95-99.7 rule, describes how data is distributed in a normal (bell-shaped) distribution:

• 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.

Given the information:

• Mean (μ) = 55
• Standard Deviation (σ) = 8

Step 1: Find the range for 1 standard deviation

The empirical rule states that 68% of the data falls within 1 standard deviation of the mean. This means:

• Lower bound: $\mu - \sigma = 55 - 8 = 47$
• Upper bound: $\mu + \sigma = 55 + 8 = 63$

Step 2: Determine the percentage of phone calls between 47 and 63

Since 47 and 63 are exactly 1 standard deviation below and above the mean, the percentage of daily phone calls numbering between these two values is 68%.

Final Answer:

The percentage of daily phone calls answered between 47 and 63 is 68%.

Would you like more details on the empirical rule or its application? Here are some related questions that could expand your understanding:

1. What is the percentage of phone calls answered between 39 and 71?
2. How many receptionists are expected to answer between 47 and 63 calls daily?
3. What percentage of receptionists answer more than 63 calls daily?
4. What is the probability of a receptionist answering fewer than 47 calls?
5. How does the empirical rule change if the standard deviation is different?

Tip: The empirical rule is very useful for quick estimates in normally distributed data without needing detailed calculations or statistical software.