In a mid size company in Boston the distribution of the number of phone calls answered each day by each of the 12 receptionist is bell-shaped and has a mean of 55 and a standard deviation of 8 using the empirical rule 68-95-99.7 what is the percentage of daily phonecalls numbering between 47 and 63

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.

Learn how to calculate the percentage of daily phone calls between 47 and 63 for a normally distributed data set with a mean of 55 and a standard deviation of 8. This problem applies the empirical rule to understand data within one standard deviation. Suitable for students in Grades 10-12.

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