A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of interstate highway. Long-term 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.

(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?

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4 or more 1 3 0 21 15 14 15 P(r) = (O-E)