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Let's go through the questions using the **empirical rule** (also known as the **68-95-99.7 rule**) to solve them.

### Question 7:
The mean is 35, and the standard deviation is 9. You need to find the approximate percentage of daily phone calls between 26 and 44.

1. **Find how many standard deviations 26 and 44 are away from the mean (35)**:
   - \( 26 \) is \( 35 - 26 = 9 \), so it is 1 standard deviation below the mean (since 9 is the standard deviation).
   - \( 44 \) is \( 44 - 35 = 9 \), so it is 1 standard deviation above the mean.

2. **Use the empirical rule**:
   - According to the empirical rule, **68%** of the data lies within **1 standard deviation** of the mean.

Thus, the percentage of daily phone calls that fall between 26 and 44 is approximately **68%**.

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### Question 8:
The mean is 60, and the standard deviation is 11. You need to find the approximate percentage of daily phone calls between 27 and 93.

1. **Find how many standard deviations 27 and 93 are away from the mean (60)**:
   - \( 27 \) is \( 60 - 27 = 33 \), which is \( 33 \div 11 = 3 \) standard deviations below the mean.
   - \( 93 \) is \( 93 - 60 = 33 \), which is \( 33 \div 11 = 3 \) standard deviations above the mean.

2. **Use the empirical rule**:
   - According to the empirical rule, **99.7%** of the data lies within **3 standard deviations** of the mean.

Thus, the percentage of daily phone calls that fall between 27 and 93 is approximately **99.7%**.

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Would you like more details on these calculations or any further explanations?

### 5 Related Questions:
1. How does the empirical rule apply to non-normal distributions?
2. What is the probability of a phone call count being more than 2 standard deviations away from the mean?
3. Can the empirical rule be used for skewed distributions?
4. How do you calculate percentages for ranges that aren't exact standard deviations from the mean?
5. How does the empirical rule relate to z-scores?

### Tip:
When using the empirical rule, always ensure that the distribution is approximately normal (bell-shaped) to get accurate approximations.

In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped. Find the approximate percentage of daily phone calls between given ranges using the empirical rule.

This problem demonstrates how to use the empirical rule to calculate the percentage of daily phone calls within specific ranges based on a bell-shaped normal distribution. Suitable for high school students, it covers statistics concepts like mean, standard deviation, and the 68-95-99.7 rule.

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