The physical plant at the main campus of a large state university receives daily requests to replace florescent light bulbs. the distribution of the number of daily requests 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 approximate percentage of the lightbulb replacements requests numbering between 47 and 55

The empirical rule (also known as the 68-95-99.7 rule) states that for a normal distribution:

- About 68% of the data falls within one standard deviation of the mean.
- About 95% falls within two standard deviations.
- About 99.7% falls within three standard deviations.

Given:
- Mean (μ) = 55
- Standard deviation (σ) = 8

We need to find the approximate percentage of requests between 47 and 55. First, let's express the range 47 to 55 in terms of standard deviations from the mean:

\[
47 = 55 - 8 \quad \text{(which is one standard deviation below the mean)}
\]
\[
55 = \mu \quad \text{(this is the mean itself)}
\]

So, the interval from 47 to 55 covers the range from one standard deviation below the mean to the mean itself. Since the empirical rule tells us that 68% of the data falls within one standard deviation (from 47 to 63, in this case), half of that (i.e., from 47 to 55) will cover half of this 68% interval.

Thus, the approximate percentage of daily requests between 47 and 55 is:

\[
\frac{68\%}{2} = 34\%
\]

### Summary:
Approximately 34% of lightbulb replacement requests fall between 47 and 55.

Do you want more details or have any questions?  
Here are 5 related questions to explore:

1. What percentage of requests fall between 55 and 63?
2. What is the percentage of requests falling between 47 and 63?
3. How would the result change if the standard deviation was 10 instead of 8?
4. What percentage of daily requests are below 47?
5. What percentage of daily requests are above 63?

**Tip:** The empirical rule can be quickly applied to estimate probabilities in normally distributed data by using standard deviations.

The physical plant at the main campus of a large state university receives daily requests to replace florescent light bulbs. The distribution of the number of daily requests 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 approximate percentage of the lightbulb replacements requests numbering between 47 and 55?

Learn how to use the empirical rule (68-95-99.7 rule) to find the percentage of lightbulb replacement requests that fall between 47 and 55 at a university campus. This problem involves normal distribution, with a mean of 55 and a standard deviation of 8. A step-by-step breakdown suitable for high school students in Grades 9-12.

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