A county has been experiencing a mean of 35.935.9 motor vehicle deaths each year. Use the Poisson distribution to answer the following. a. Find the mean number of deaths per day. b. Find the probability that on a given day, there are more than 2 motor vehicle deaths. c. Is it unusual to have more than 2 motor vehicle deaths on the same day

Question

Deon Griffith

Mathematics

30 August, 05:36

A county has been experiencing a mean of 35.935.9 motor vehicle deaths each year. Use the Poisson distribution to answer the following. a. Find the mean number of deaths per day. b. Find the probability that on a given day, there are more than 2 motor vehicle deaths. c. Is it unusual to have more than 2 motor vehicle deaths on the same day

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Bennett · Answer 1

A. You are given the mean per year. Thus, just convert the unit of time from year to day.

Mean per day = 35.935.9/year * 1 year/365 days = 98.45

b. Probability is expressed as a fraction or percentage of an event happening. In this case, we should determine when each day, the amount of accidents is 3, 4, 5, 6, and so on. It would be much easier to find the probability of the accident happening once or twice a day.

probability for accidents once and twice a day: 1/98.45 + 2/98.45 = 0.03

Probability for accidents more than twice a day: 1 - 0.03 = 0.97

c. It is not unusual due to the high probability of it happening as quantified in letter b.