Question 1173159: Suppose that on a highway, an average of four accidents occur per day.
a) State the parameter for this probability distribution.
b) Calculate the mean and standard deviation for this probability distribution.
c) What is the probability that an accident will occur on a particular day?
d) Find the probability that from 4 to 6 accidents will occur from 1:00pm to 7:00pm on a particular day.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! This is a Poisson distribution- counts, proportional to time, could theoretically be infinite.
Parameter is 4.
Mean is 4 accidents a day, variance is 4 acc^2/day^2 and SD is 2 accidents/day
that is 1-probability no accidents occurs on a day. The latter is e^(-4) or 0.0183, so the answer is 1-0.0183 or 0.9817.
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A 6 hour period would be expected to have 1 accident during that time, since it is 1/4 of a day so 1/4 of 4 accidents is 1.
Instead of e^(-4)*4^k/k! we have scaled it down to 1/4 of that so the distribution is e^(-1)*1^k/k!
p(4)=e^(-1)1^4/4!=0.0153
p(5)=e^(-1)*1^5/120=0.0031
p(6)=0.0005 (the denominator is 6! or 720.
The overall probability is 0.0189.
This would be low probability, because one would be expecting the usual number of daily accidents to occur in 1/4 of the time.
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