The average number of cars per hour arriving at a toll booth is 57 while the...
The average number of cars per hour arriving at a toll booth is 57 while the standard deviation is 15.
(a) Use Markov’s inequality to find an upper bound on the probability of having more than 200 cars arrive in an hour.
(b) Use Chebyshev’s inequality to find an upper bound on the probability of having more than 200 cars arrive in an hour
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The average number of cars per hour arriving at a toll booth is
57 while the...
Cars arrive at a toll booth at average rate of 60 per hour. The standard deviation...
Cars arrive at a toll booth at average rate of 60 per hour. The standard deviation of the time between arrivals is 0.8 minutes. What is the coefficient of variation of the interarrival times of cars?
The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with...
The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 5 cars arriving over a five-minute interval is __________ . Group of answer choices 0.0940 0.0417 0.1500 0.1008 0.2890
An average of 90 cars per hour arrive at a single-server toll booth. The average service...
An average of 90 cars per hour arrive at a single-server toll booth. The average service time for each customer is a half minute, and both interarrival times and service times are exponential. For each of the following questions, show your work, including the formula that you are using. 1) On average, how many cars per hour will be served by the server
Assume the average number of cars arriving at a certain freeway entrance ramp during an hour...
Assume the average number of cars arriving at a certain freeway entrance ramp during an hour is 5. What is the probability that in a given hour no cars will arrive at the ramp? a. What is the probability that exactly 5 cars will arrive in an hour. b. What is the probability that more than 5 cars will arrive in an hour?
7.1. Cars arrive to a toll booth 24 hours per day according to a Poisson process...
7.1. Cars arrive to a toll booth 24 hours per day according to a Poisson process with a mean rate of 15 per hour. (a) What is the expected number of cars that will arrive to the booth between 1:00 p.m. and 1:30 p.m.? (b) What is the expected length of time between two consecutively arriving cars! (c) It is now 1:12 p.m. and a car has just arrived. What is the expected number of cars that will arrive between...
1) A toll plaza has 5 booths, with each booth capable of servicing 50 cars per...
1) A toll plaza has 5 booths, with each booth capable of servicing 50 cars per hour. Cars arrive at the plaza at the rate of 225 cars per hour. Make the standard assumptions of a Poisson distribution for arrivals, and an Exponential distribution for service times, and calculate the following: a) What is the probability of zero cars in the toll plaza? b) What is the average length (in cars) of the (total) queue?
2. The number of cars passing through each lane of a toll booth per minute is...
2. The number of cars passing through each lane of a toll booth per minute is represented by a random variable, C, and the number of trucks passing through it is represented by another random variable, T. During the morning peak hour, the joint probability mass function of C and T is given by the following table 0 0.05 0.08 0.08 1 0.05 0.09 0.11 0.08 0.22 0.11 0.06 0.05 0.02 Find the marginal probability mass function of T, pr(t)...
Ass 10. On the average, 10 cars arrive at the drive-up window of a bank every hour. Define the random variable X to...
Ass 10. On the average, 10 cars arrive at the drive-up window of a bank every hour. Define the random variable X to be the number of cars arriving in any hour. a. Calculate the probability that less than 6 cars arrive in the next hour b. Compute the probability that exactly 5 cars will arrive in the next hour. C. Compute the probability that no more than 5 cars will arrive in the next hour.
(20) 13. The number of people arriving at a doctor’s office is 4 per hour. Let...
(20) 13. The number of people arriving at a doctor’s office is 4 per hour. Let x represent the number of people arriving per hour. (5) a. What is the probability that exactly 4 people arrive in one hour? Show how you calculated this. (5) b. What is the probability that less than 2 people arrive in one hour? Show how you calculated this. (5) c. What is the probability that less than 3 people arrive in one hour? Show...
The number of customers arriving per hour at a certain automobile service facility is assumed to...
The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean λ = 6. (a) Compute the probability that more than 20 customers will arrive in a 3-hour period. (b) What is the probability that the number of customers arriving in a 2-hour period will not exceed 40? (c) What is the mean number of arrivals during a 4-hour period?
Cars arrive at a toll booth at average rate of 60 per hour. The standard deviation of the time between arrivals is 0.8 minutes. What is the coefficient of variation of the interarrival times of cars?
7.1. Cars arrive to a toll booth 24 hours per day according to a Poisson process with a mean rate of 15 per hour. (a) What is the expected number of cars that will arrive to the booth between 1:00 p.m. and 1:30 p.m.? (b) What is the expected length of time between two consecutively arriving cars! (c) It is now 1:12 p.m. and a car has just arrived. What is the expected number of cars that will arrive between...
2. The number of cars passing through each lane of a toll booth per minute is represented by a random variable, C, and the number of trucks passing through it is represented by another random variable, T. During the morning peak hour, the joint probability mass function of C and T is given by the following table 0 0.05 0.08 0.08 1 0.05 0.09 0.11 0.08 0.22 0.11 0.06 0.05 0.02 Find the marginal probability mass function of T, pr(t)...
Ass 10. On the average, 10 cars arrive at the drive-up window of a bank every hour. Define the random variable X to be the number of cars arriving in any hour. a. Calculate the probability that less than 6 cars arrive in the next hour b. Compute the probability that exactly 5 cars will arrive in the next hour. C. Compute the probability that no more than 5 cars will arrive in the next hour.
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