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 1.68 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 19 22 17 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 λr r! Here λ = 1.68 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(1) = 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(1) = E(2) = E(3) = E(4 or more) = (c) Compute the sample statistic Χ2 = Σ((O – E)2/E) and the degrees of freedom. (Round your sample statistic to three decimal places.) df = Χ2 =
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 1.68 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 19 22 17 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 λr r! Here λ = 1.68 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(1) = 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(1) = E(2) = E(3) = E(4 or more) = (c) Compute the sample statistic Χ2 = Σ((O – E)2/E) and the degrees of freedom. (Round your sample statistic to three decimal places.) df = Χ2 =
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
Related questions
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 1.68 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 | 19 | 22 | 17 | 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.
Here λ = 1.68 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.)
P(r) =
| e−λ λr |
| r! |
| P(0) = | |
| P(1) = | |
| 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(1) = | |
| E(2) = | |
| E(3) = | |
| E(4 or more) = |
(c) Compute the sample statistic Χ2 = Σ((O – E)2/E) and the degrees of freedom. (Round your sample statistic to three decimal places.)
| df = | |
| Χ2 = |
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