Acivil 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 accidents per day on this section of the interstate. let be a random variable that represents number of accidents per day. let represent the number of observed accidents per day based on local highway patrol reports. a random sample of days gave the following information.
r 0 1 2 3 4 or more
o 19 23 16 18 14
(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 given below. p(r) = (e^−λ) λ^r/r!
here λ = 1.79 is the average number of accidents per day. compute p(r) for r = 0, 1, 2, 3, and 4 or more. (round your answers to three decimal places.)
b) compute the expected number of accidents e = 90p(r) for r = 0, 1, 2, 3, and 4 or more. (round your answers to two decimal places.)
(c) compute the sample statistic χ2 = σ((o – e)2/e) and the degrees of freedom. (round your sample statistic to three decimal places.)