# Poisson: Deaths Currently, an average of 7 residents of the village of Westport (population 760) die each year (based on data from the U.S. National Center for Health Statistics).a. Find the mean number of deaths per day.b. Find the probability that on a given day, there are no deaths.c. Find the probability that on a given day, there is more than one death.d. Based on the preceding results, should Westport have a contingency plan to handle more than one death per day? Why or why not?

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Asked Jan 21, 2020
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Poisson: Deaths Currently, an average of 7 residents of the village of Westport (population 760) die each year (based on data from the U.S. National Center for Health Statistics).

a. Find the mean number of deaths per day.

b. Find the probability that on a given day, there are no deaths.

c. Find the probability that on a given day, there is more than one death.

d. Based on the preceding results, should Westport have a contingency plan to handle more than one death per day? Why or why not?

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## Expert Answer

Step 1

(a)

Define the random variable x as the number of deaths per year. Here, the average number of deaths per year is 7 and each death is independent of the other. Hence, the random variable follows the Poisson distribution.

Step 2

Thus, the mean number of deaths in a given day is 0.0192 deaths.

(b)

Define the random variable x as the number of deaths per day. Here, the numbers of deaths are random and each death is independent of the other. Also, the occurrences (death) are uniformly distributed. Then, x follows a Poisson distribution.

Step 3

Interpretation:

There is 98% chance of having no deaths on a given day.

(c)

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