A civil engineer has been studying the frequency of vehicle accidents on a certa

Question

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 1.80 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. 4 or more (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) r! Here ? 1.80 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.) P(0) P(2) P(3) P(4 or more) (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.) E(0)- E(2) E(3) E(4 or more) - (c) Compute the sample statistic X2 = ?((0-E)2/E) and the degrees of freedom. (Round your sample statistic to three decimal places.)

Explanation / Answer

Ans a Using the formula given for Poisson Process

P(0) = 0.165

P(1) = 0.296

P(2) = 0.268

P(3) = 0.161

P(4 or more) = 1 - { P(0) + P(1) + P(2) + P(3) }

1 - 0.89 = 0.11

Ansb = From the Given Formula

E (0) = 14.85

E(1) = 26.64

E(2) = 24.12

E(3) = 14.49

E(4 or more) = 9.9

Ans c The value of df is no.of classes -1 = 5-1 = 4

And value of X2 = 2.547 + 0.808 + 4.246 + 0.435 + 3.759 = 11.795

Please give upvote if you find the answer helpful.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.