The problem provided refers to a bell-shaped (normal) distribution of daily lightbulb replacement requests, with a mean of 60 and a standard deviation of 11. You are asked to find the approximate percentage of requests between 60 and 71 using the Empirical Rule.

Step-by-Step Solution:

1. Empirical Rule Overview:

   • In a normal distribution:
     • 68% of the data lies within 1 standard deviation of the mean (i.e., between $\mu - \sigma$ and $\mu + \sigma$).
     • 95% lies within 2 standard deviations.
     • 99.7% lies within 3 standard deviations.

2. Given:

   • Mean ($\mu$) = 60
   • Standard deviation ($\sigma$) = 11
   • We are asked to find the percentage between 60 and 71.

3. Identify the Range:

   • The lower bound is 60, which is exactly the mean ($\mu$).
   • The upper bound is 71. To calculate how far this is from the mean in terms of standard deviations: $Z = \frac{71 - 60}{11} = \frac{11}{11} = 1$
   • Therefore, the range is between the mean ($\mu$) and one standard deviation above the mean ($\mu + \sigma$).

4. Empirical Rule Application:

   • The Empirical Rule tells us that 68% of the data lies within 1 standard deviation from the mean (from $\mu - \sigma$ to $\mu + \sigma$).
   • Since the question asks for the percentage between 60 and 71 (from $\mu$ to $\mu + \sigma$), this is half of the 68%, because it only concerns the portion above the mean.
   • Therefore, the percentage is: $\frac{68}{2} = 34\%$

Final Answer:

The approximate percentage of requests between 60 and 71 is 34%.

Do you want further details or have any questions? Here are some related questions you might find helpful:

1. What is the Empirical Rule and how is it applied in statistics?
2. How would the percentage change if the range was from 49 to 71?
3. What is the difference between a Z-score and the Empirical Rule?
4. How can I calculate percentages for non-standard deviations in a normal distribution?
5. What would the answer be if the range were from 60 to 82 instead?

Tip: The Empirical Rule is an approximation used for quick estimates in a normal distribution. For precise values, Z-scores and normal distribution tables are used.