SOLUTION: Data for 7 corps were combined for the 20-year period, and the 140 corps-years included a total of 84 deaths. Suppose the Poisson distribution will be used to find the probability

Question 765339: Data for 7 corps were combined for the 20-year period, and the 140 corps-years included a total of 84 deaths. Suppose the Poisson distribution will be used to find the probability that a randomly selected corps-year has more than 4 deaths. Find the mean of the appropriate Poisson distribution (the mean number of deaths per corps-year)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you have 7 corps that have a total of 84 deaths in a 20 year period.
7 corps times 20 years equals 140 corps years.
poisson distribution is assumed.
the poisson distribution formula is:

p(r,x = r^x / (e^r * x!)

r is the average rate per period
x is the number of occurrences you are looking for.
in your problem, r is equal to 84 / 120 = .7 deaths per corps year.
in your problem, x is equal to 4 corps deaths per corps year.
since the answer you are looking for is a cumulative distribution smaller than x, you need a table or a calclator to find your answer.
here's a calculator from stattrek that gives you all possible occurrences.
http://stattrek.com/online-calculator/poisson.aspx
enter 4 for x and enter .7 for average rate of death per corps year.
press the calculate button and your answers appear.
in that calculator, x is equal to the number of occurrences per time period you are looking for and X is equal to the probability of getting that many occurrences, or less than that many occurrences, or more than that many occurrences, or less than or equal to that many occurrences, etc.
p(X = 4) is equal to .004968
p(X > 4) is equal to .000786
p(X >= 4 is equal to .005753
the answer to your problem is p(X > 4) = .000786.
i confirmed the calculator's results using the ti-84+ calculator and i get the same answers, so i assume the calculator is providing you with accurate results.
here's a table that will provide you with the same answer after a bit of manipulation.
http://mat.iitm.ac.in/home/vetri/public_html/statistics/poisson.pdf
you have to find p(X <= x) and then take 1 minus that probsability to get p(X > x).
the easiest way, by far, is to use the stattrek calculator shown above.
a decent reference on the subject is:
http://stattrek.com/probability-distributions/poisson.aspx

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