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Question

# U.S. airlines average about 4.5 fatalities per month. (Statistical Abstract of the United States: 2012). Assume that the probability distribution for x, the number of fatalities per month, can be approximated by a Poisson probability distribution. a. What is the probability that no fatalities will occur during any given month? b. What is the probability that one fatality will occur during any given month? c. Find E(x) and the standard deviation of x.

Solution

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Given:

$\lambda=\mu=\text{Average}=4.5$

(a) Formula $\textbf{Poisson probability}$:

$P(x=k)=\dfrac{\lambda^k e^{-\lambda}}{k!}$

Evaluate the formula of Poisson probability at $k=0$:

\begin{align*} P(x=0)&=\dfrac{4.5^0 e^{-4.5}}{0!}=e^{-4.5}\approx 0.0111=1.11\% \end{align*}

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