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 1.66 accidentsp 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 patro A random sample of 90 days gave the following information. 3 4 or more 21 19 18 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) = r! Here i = 1.66 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) = Е(3) %3D E(4 or more) =

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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 1.66 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
1
4 or more
21
19
18
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.
е
P(r) :
r!
Here 1
1.66 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.)
Р(0)
P(1)
P(2)
Р(3)
%3D
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.)
%3D
E(0) =
E(1) =
%3D
Е(2) :
Е(3) -
E(4 or more) =
%3D
(c) Compute the sample statistic X2
E((0 - E)IE) and the degrees of freedom. (Round your sample statistic to three decimal places.)
df =
x2
Transcribed Image Text: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 1.66 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 1 4 or more 21 19 18 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. е P(r) : r! Here 1 1.66 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.) Р(0) P(1) P(2) Р(3) %3D 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.) %3D E(0) = E(1) = %3D Е(2) : Е(3) - E(4 or more) = %3D (c) Compute the sample statistic X2 E((0 - E)IE) and the degrees of freedom. (Round your sample statistic to three decimal places.) df = x2
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