A certain traffic intersection has on average 2.2 motor vehicle accidents per we

ID: 3379781 • Letter: A

Question

A certain traffic intersection has on average 2.2 motor vehicle accidents per week. Assume that accidents occur independently at this intersection.

1. Let A be the number of accidents that occur in a week. What are the distribution, parameter(s), and support of A? (3 points)

2. What is the probability that there is at most 1 accident in the first week of November? (3 points)

3. What is the probability that there are 2 accidents in the first week of November and 4 accidents in the second week of November? (3 points)

4. Assuming there are four weeks in a month, what is the average number of accidents in the month of November? (2 points)

5. What is the probability that there are 12 accidents in the month of November? What distribution and parameter(s) are you using? (4 points)

A is Poisson with mean = 2.2

2) P(X<=1) = 0.3546

3) P(X=2 in first week and x=4 in second week)

P(X=1 in first week)* P( x=4 in second week) (as the two events are independent)

= 0.2438(0.2681)

= 0.0654

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4) Average number of accidents in November

= 4 x average per week

= 8.8

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5) P(X=12 in November for average 8.8)

= 0.0679

Distribution is Poisson with mean = 8.8

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