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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

VerifiedAnswered 11 months ago

Answered 11 months ago

Step 1

1 of 7Given: Poisson random variable

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

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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