APFIVE Conditions For Using The Empirical Rule
Assuming a normal distribution for New York City taxi mileage data, a researcher applied the empirical rule and stated that 68% of taxis are driven between $$75000 - 12000 = 63000$$ and $$75000 + 12000 = 87000$$ miles. However, later examination revealed that the mileage data were skewed. What mistake did the researcher make when applying the empirical rule?
Taxi Mileage Summary
| Statistic | Value |
|---|---|
| Mean ($$\mu$$) | 75000 |
| Standard Deviation ($$\sigma$$) | 12000 |
| (Other details omitted) |
A
He used the median instead of the mean for the empirical rule calculations.
B
He assumed normality and applied the empirical rule without verifying that the data distribution was approximately normal.
C
He incorrectly recalculated the boundaries by using the range rather than the standard deviation.
D
He multiplied the mean by the standard deviation instead of adding and subtracting.
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