Question

Public transit deaths. Millions of suburban commuters use the public transit system (e.g., subway trains) as an alternative to the automobile. While generally perceived as a safe mode of transportation, the average number of deaths per week due to public transit accidents is 5 (Bureau of Transportation Statistics, 2015). Based strictly on your answers to part b, is it likely that more than 12 deaths occur next week? Explain.

Solution

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Answered 11 months ago
Answered 11 months ago
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Given: Poisson random variable

λ=μ=Mean=5\begin{aligned} \lambda&=\mu=\text{Mean}=5 \end{aligned}

We need to determine whether more than 12 deaths are likely to occur.

Chebyshev's Rule tells us that:

  • At least none of the data values are within one standard deviation of the mean.
  • At least 3/4 or 75% of the data values are within two standard deviations of the mean.
  • At least 8/9 or about 89% of the data values are within three standard deviations of the mean.

Thus nearly all data values are expected to be within 3 standard deviations of the mean.

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