Highway Accidents: Poisson Distribution A civil engineer

Chapter , Problem 17

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Highway Accidents: Poisson Distribution A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of interstate highway. Longterm history indicates that there has been an average of 1.72 accidents per day on this section of the interstate. Let r be a random variable that represents number of accidents per day. Let O represent the number of observed accidents per day based on local highway patrol reports. A random sample of 90 days gave the following information. r 0 1 2 3 4 or more O 22 21 15 17 15 (a) The civil engineer wants to use a Poisson distribution to represent the probability of r, the number of accidents per day. The Poisson distribution is where l 1.72 is the average number of accidents per day. Compute P(r) for r 0, 1, 2, 3, and 4 or more. (b) Compute the expected number of accidents E 90P(r) for r 0, 1, 2, 3, and 4 or more. (c) Compute the sample statistic and the degrees of freedom. (d) Test the statement that the Poisson distribution fits the sample data. Use a 1% level of significance.