Question
In: Statistics and Probability
The truck traffic on a highway can be describe as a Poisson process with a mean...
The truck traffic on a highway can be describe as a Poisson
process with a mean arrival rate of 1.5 trucks per minute. The
weight of each truck is random and the probability that a truck is
overloaded is 5%.
a. What is the probability that there will be at least
two trucks passing a weigh stat ion this highway in a 10-minute
period? Define the random variable.
b. What is the probability that at most one of the next
10 trucks stopping at the weigh station will be overloaded? Define
the random variable.
c. Suppose the weigh station will close for 30 minutes
for lunch. What is the probability of overloaded trucks passing the
weigh station during the lunch break? Define the random
variable.
Solutions
orchestra answered 2 years agoRelated Solutions
The traffic incidents in Melbourne and Sydney follow a Poisson process with the rate of 5...
The traffic incidents in Melbourne and Sydney follow a Poisson
process with the rate
of 5 and 6 incidents per hour, respectively.
(a) Find the probability that no traffic accidents will occur in
Melbourne in the next
30 minutes.
(b) Find the expected time (in minutes) until 10 new incidents
occur in Sydney.
(c) Find the expected time (in minutes) until 10 new incidents in
total occur in
Melbourne and Sydney. Hint: For this and the next question, you can...
The traffic incidents in Melbourne and Sydney follow a Poisson process with the rate of 5...
The traffic incidents in Melbourne and Sydney follow a Poisson
process with the rate
of 5 and 6 incidents per hour, respectively.
(a) Find the probability that no traffic accidents will occur in
Melbourne in the next
30 minutes.
(b) Find the expected time (in minutes) until 10 new incidents
occur in Sydney.
(c) Find the expected time (in minutes) until 10 new incidents in
total occur in
Melbourne and Sydney. Hint: For this and the next question, you can...
5. The occurrence of traffic accidents at an intersection is modeled as a Poisson process. Based...
5. The occurrence of traffic accidents at an intersection is
modeled as a Poisson process. Based on accident records at that
intersection, a traffic engineer has determined that the average
rate of accidents occurring at that intersection is once every
three years.
(a) What is the probability that no accident occurs at that
intersection for a period of 5 years?
(b) What is the probability that there is a traffic fatality at
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On a highway, vehicles pass according to a Poisson process with rate 1 vehicle per minute....
On a highway, vehicles pass according to a Poisson process with
rate 1 vehicle per minute. Suppose that 25% of the vehicles
are trucks and 75% of the vehicles are cars. Let
NC(t) and NT(t) denote the number of cars and
trucks that pass in t minutes, respectively. Then N(t) =
NC(t) + NT(t) is the number of vehicles that
pass in t minutes.
Find E[N(10) | NT(10)=2]
Find P[NC(10)=14 | N(10)=15]
Traffic flow is traditionally modeled as a Poisson Distribution. A traffic engineer monitors the traffic flowing...
Traffic flow is traditionally modeled as a Poisson Distribution.
A traffic engineer monitors the traffic flowing through an
intersection with an average of 9 vehicles per minute.
What is the random variable X described above? Write the
distribution of X using the standard notations.
What should be the variance and the standard deviation of the
number of vehicles through the intersection within a minute?
...
Traffic on Rosedale Road in Princeton, NJ, follows a Poisson process with rate 6 cars per...
Traffic on Rosedale Road in Princeton, NJ, follows a Poisson
process with rate 6 cars per minute. A deer runs out of the woods
and tries to cross the road. It takes the deer a random time
(independent of everything else), uniformly distributed between 2
and 5 seconds, to cross the road. If there is a car passing while
the deer is on the road, it will hit the deer with portability 2/3
(independent of everything else). Find the probability...
The National Highway Traffic Safety Administration reported the percentage of traffic accidents occurring each day of...
The National Highway Traffic Safety Administration reported the
percentage of traffic accidents occurring each day of the week.
Assume that a sample of 420 accidents provided the following
data.
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
66
50
52
47
56
69
80
(a) Conduct a hypothesis test to determine if the proportion of
traffic accidents is the same for each day of the week. Use a 0.05
level of significance.
State the null and alternative hypotheses:
A. H0: Not...
The National Highway Traffic Safety Administration reported the percentage of traffic accidents occurring each day of...
The National Highway Traffic Safety Administration reported the
percentage of traffic accidents occurring each day of the week.
Assume that a sample of 420 accidents provided the following data.
Sunday 63. Monday 47. Tuesday 55. Wednesday 45. Thursday 57. Friday
67. Saturday 86. 1)Conduct a hypothesis test to determine if the
proportion of traffic accidents is the same for each day of the
week. What is the p-value? 2. Compute the value of the x^2 test
statistic (to 3 decimals)....
The National Highway Traffic Safety Administration reports the percentage of traffic accidents occurring each day of...
The National Highway Traffic Safety Administration reports the
percentage of traffic accidents occurring each day of the week.
Assume that a sample of 420 accidents provided the following
date.
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Total
66
50
53
47
55
69
80
420
Conduct a hypothesis test to determine whether the proportion of
traffic accidents is the same for each day of the week. Using a .05
level of significance, what is your conclusion?
1. Which is the...
The National Highway Traffic Safety Administration reported the percentage of traffic accidents occurring each day of...
The National Highway Traffic Safety Administration reported the
percentage of traffic accidents occurring each day of the week.
Assume that a sample of 420 accidents provided the following
data.
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
66
50
53
48
54
69
80
(a)
Conduct a hypothesis test to determine if the proportion of
traffic accidents is the same for each day of the week. Use a 0.05
level of significance.
State the null and alternative hypotheses.
H0: pSun =...
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