The life spans of three randomly selected tires are 

28,100 
miles, 
37,900 
miles, and 
33,000 
miles. Using the empirical rule, find the percentile that corresponds to each life span.

Insufficient data. Mean? Standard deviation?

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability below each Z value. Multiply by 100.

To find the percentiles that correspond to each life span using the empirical rule, we need to calculate the Z-scores for each tire's life span and then use a Z-table to find the corresponding percentiles.

The empirical rule, also known as the 68-95-99.7 rule, states that for a normally distributed data set:
- Approximately 68% of the data falls within one standard deviation of the mean
- Approximately 95% of the data falls within two standard deviations of the mean
- Approximately 99.7% of the data falls within three standard deviations of the mean

Here's how we can calculate the percentiles:

1. Find the mean and standard deviation of the data set:
- Mean (μ): (28,100 + 37,900 + 33,000) / 3 = 33,000 miles
- Standard Deviation (σ): Calculate the sample standard deviation

2. Calculate the Z-score for each tire's life span:
- Z-score = (X - μ) / σ, where X is the individual life span of each tire

For the first tire: Z1 = (28,100 - 33,000) / σ
For the second tire: Z2 = (37,900 - 33,000) / σ
For the third tire: Z3 = (33,000 - 33,000) / σ

3. Use a Z-table or a Z-score calculator to find the percentiles for each Z-score. The Z-table provides the cumulative probability (percentile) for each Z-score.
- The percentile is the probability that a randomly selected observation from a distribution is less than or equal to that particular value.

Once you have the Z-scores for each tire's life span, you can use the Z-table to find the corresponding percentiles.