Highway Accidents: Poisson Distribution 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.

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 P r e

r

r 5

2l

( )

!

where l 51.72 is the average number of accidents per day. Compute P(r) for r 5 0, 1, 2, 3, and 4 or more.

(b) Compute the expected number of accidents E 5 90P(r) for r 5 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.AppendixLO1

Transcribed Image Text:

x = (0 - E) E