Vehicles have been arriving at a toll bridge at an average rate of 216 an hour....
Vehicles have been arriving at a toll bridge at an average rate of 216 an hour. Only one toll booth is currently open and can process arrivals (collect tolls) at a mean rate of 20 seconds per vehicle. a. How many vehicles should be expected at the toll bridge in a 10-minute period? Please show how you arrived at your answer. b. Define X to be the number of vehicles arriving at the toll bridge in a 10-minute period and assume that X has a Poisson Probability distribution. Please calculate the probability that exactly 30 vehicles will arrive at the toll bridge in a 10-minute period. c. Please calculate the probability of at most 25 vehicles arriving at the bridge within 10-minute period. d. Please calculate the probability of more than 40 vehicles arriving at the bridge within 10-minute period. e. Please calculate the probability of fewer than 20 vehicles arriving at the bridge within a 10-minute period. f. Please calculate the probability of at least 25 vehicles arriving at the bridge within a 10-minute period. Show your work. g. Please calculate the probability of no vehicle arriving at the bridge within a 10-minute period. Show your work. h. Calculate and interpret the standard deviation of X. i. For what purpose can the kind of information you have calculated above be used? If the state department of transportation wants to reduce the average wait time for the drivers to less than 22 seconds at the toll bridge, do you think they should open anther toll booth at the bridge? Please carefully justify your answer.
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Vehicles have been arriving at a toll bridge at an average rate
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QUESTION 26 At an entrance to a toll bridge, four toll booths are open. Vehicles arrive...
QUESTION 26 At an entrance to a toll bridge, four toll booths are open. Vehicles arrive at the bridge at an average rate of 900 veh/h, and at the booths, drivers take an average of 12 seconds to pay their tolls. Both the arrival and departure headways can be assumed to be exponentially distributed How would the average queue length change if a fifth toll booth were opened? a. The average queue length is reduced by 1.17 vehicles D.The average...
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
Autos arrive at a toll plaza located at the entrance to a bridge at a rate...
Autos arrive at a toll plaza located at the entrance to a bridge at a rate of 10 per minute during the 5:00-to-6:00 P.M. hour. Determine the following probabiiies assuming that an auto has just arrived. a. What is the probability that the next auto will arrive within 6 seconds (0.1 minute)? b. What is the probability that the next auto will arrive within 3 seconds (0.05 minute)? c. What are the answers to (a) and (b) if the rate...
the Ponchatrain Bridge is a 16-mile toll bridge that crosses Lake Ponchatrain in New Orleans. Currently,...
the Ponchatrain Bridge is a 16-mile toll bridge that crosses Lake Ponchatrain in New Orleans. Currently, there are 7 toll booths, each staffed by an employee. Since Hurricane Katrina, the Port Authority has been considering replacing the employees with machines. Many factors must be considered because the employees are unionized. However, one of the Port Authority's concerns is the effect that replacing the employees with machines will have on the times that drivers spend in the system. Customers arrive...
Automobiles arrive at a toll plaza located at the entrance to a bridge at a rate...
Automobiles arrive at a toll plaza located at the entrance to a bridge at a rate of 51 per minute during the 5:00 to 6:00 p.m. hour (assume Exponential distribution). If an auto has just arrived, what is the probability: a) That the next auto will arrive within 3 seconds? b) That the next auto will arrive in the next 3 to 10 seconds? c) That the next auto will arrive after 2 seconds?
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
The average number of customers arriving at a drive-through window of a bank branch is 39...
The average number of customers arriving at a drive-through window of a bank branch is 39 per hour during lunch hours. Use X to denote the number of arrivals in a 5 minute time interval. Assume the customers arrive independently and the number of arrivals within each 5 minutes follows a Poisson distribution. Keep at least 4 decimal digits if the result has more decimal digits. I AM JUST LOOKING FOR WHAT FUNCTION/EQUATION TO PUT INTO MY CALCULATOR TO GET...
The mean arrival rate of vehicles (Poisson process) is 1.08 (based on previous observations). Assume that...
The mean arrival rate of vehicles (Poisson process) is 1.08 (based on previous observations). Assume that the minimum arrival rate is 10% less than the estimated value 1.08), and that maximum arrival rate is 10% greater than the estimated value 1.08). Hence there are three arrival rate estimates (min, expected, and max). Assume that these three value are equally likely (0.333 probability each). Given that you next observe the following 6toll booth vehicle arrival data, per minute - 2,2,2,2,4,3. Draw...
Please answer all four parts of the question and show all work. Thank you! Given an...
Please answer all four parts of the question and show all work. Thank you! Given an arrival rate (lambda and in terms “so many arrivals per time unit) and an X, where X is defined on the same time unit as lambda, that is, if lambda is 20 per hour, then X is not 5 minutes, it is 5/60 of an hour). Prob (next arrival less than X) = 1- e-λX Autos arrive at a toll plaza at a rate...
4. The emergency telephone (911) center in a large city receives an average of 210 calls...
4. The emergency telephone (911) center in a large city receives an average of 210 calls per hour during a typical day. On average, each call requires about 121 seconds fora dispatcher to receive the emergency call, determine the nature and location of the problem, and send the required individuals (police, firefighters, or ambulance) to the scene. The center is currently staffed by 7 dispatchers a shift but must have an adequate number of dispatchers on duty and it has...
QUESTION 26 At an entrance to a toll bridge, four toll booths are open. Vehicles arrive at the bridge at an average rate of 900 veh/h, and at the booths, drivers take an average of 12 seconds to pay their tolls. Both the arrival and departure headways can be assumed to be exponentially distributed How would the average queue length change if a fifth toll booth were opened? a. The average queue length is reduced by 1.17 vehicles D.The average...
Autos arrive at a toll plaza located at the entrance to a bridge at a rate of 10 per minute during the 5:00-to-6:00 P.M. hour. Determine the following probabiiies assuming that an auto has just arrived. a. What is the probability that the next auto will arrive within 6 seconds (0.1 minute)? b. What is the probability that the next auto will arrive within 3 seconds (0.05 minute)? c. What are the answers to (a) and (b) if the rate...
4. The emergency telephone (911) center in a large city receives an average of 210 calls per hour during a typical day. On average, each call requires about 121 seconds fora dispatcher to receive the emergency call, determine the nature and location of the problem, and send the required individuals (police, firefighters, or ambulance) to the scene. The center is currently staffed by 7 dispatchers a shift but must have an adequate number of dispatchers on duty and it has...
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