Question

In: Statistics and Probability

Passengers arriving into Pearson International Airport are to have their temperature check before leaving the airport....

Passengers arriving into Pearson International Airport are to have their temperature check before leaving the airport. Any passengers with a fever are required to go into quarantine. Three Nurses perform the check. An average of 3.84 passengers per minute arrive at the checkpoint and wait in a single line. They are checked by the first available nurse. It takes on average 25 seconds to check a passenger. Assume that inter-arrival times and service times are exponential distribute, FCFS, infinite queue, infinite population size.

(a) What is the probability that a passenger will not have to wait when they arrive at the checkpoint? (6 marks)

(b) On average, how many passengers will be at the checkpoint (waiting & being scanned)? (4 marks)

(c) When the passenger finally reaches the checkpoint, what is the probability it will take 20 seconds or less to check their temperature?

(d) What is the probability there will be more than 2 passengers arriving to the checkpoint in a one min time period.

Solutions

Expert Solution

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Problem 1 Passengers arriving into Pearson International Airport are to have their temperature check before leaving...
Problem 1 Passengers arriving into Pearson International Airport are to have their temperature check before leaving the airport. Any passengers with a fever are required to go into quarantine. Three Nurses perform the check. An average of 3.84 passengers per minute arrive at the checkpoint and wait in a single line. They are checked by the first available nurse. It takes on average 25 seconds to check a passenger. Assume that inter-arrival times and service times are exponential distribute, FCFS,...
The number of passengers arriving at a checkout counter of an international airport follows a Poisson...
The number of passengers arriving at a checkout counter of an international airport follows a Poisson distribution. On average, 4 customers arrive every 5-minutes period. The probability that over any 10-minute interval, at most 5 passengers will arrive at the checkout counter is A:- 0.1221 B:- 0.1250 C:- 0.2215 D:- 0.8088 The number of customers who enter a bank is thought to be Poisson distributed with a mean equal to 10 per hour. What are the chances that 2 or...
All airport passengers at the Capital City Airport must pass through a security screening area before...
All airport passengers at the Capital City Airport must pass through a security screening area before proceeding to the boarding area. The airport has three screening stations available, and the facility managers must decide how many to open at any particular time. The average time for processing one passenger at each screening station is 0.5 minutes. On Saturday morning the arrival rate is 3.3 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and...
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The...
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute. Compute the probability of no arrivals in a one-minute period (to 6 decimals). Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals). Compute the probability of no arrivals in a 15-second period (to 4 decimals). Compute the probability of at least one arrival in a 15-second period (to 4...
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The...
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 6 passengers per minute. A. Compute the probability of no arrivals in a one-minute period (to 6 decimals). B. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals). C. Compute the probability of no arrivals in a 15-second period (to 4 decimals). Compute the probability of at least one arrival in a 15-second...
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The...
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 6 passengers per minute. a. Compute the probability of no arrivals in a one-minute period (to 6 decimals). b. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals). c. Compute the probability of no arrivals in a 15 second period (to 4 decimals). d. Compute the probability of at least one arrival in...
A random sample of 19 airline passengers at Hartsfield Jackson International airport showed that the mean...
A random sample of 19 airline passengers at Hartsfield Jackson International airport showed that the mean time spent waiting in line to pass though the TSA checkpoint was 31 minutes with a standard deviation of 7 minutes. Construct a 95 % confidence interval for the mean waiting time by all passengers in the TSA checkpoint at this airport. Assume that such waiting time for all passengers is normally distributed. A) 31+1.65(7/P19) B) 31+1.746(7/P19) C) 31+1.96(7/P19) D ) 31+2.101(7/P19)
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The...
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is passengers per minute. a. Compute the probability of no arrivals in a one-minute period (to 6 decimals). b. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals). c. Compute the probability of no arrivals in a -second period (to 4 decimals). d. Compute the probability of at least one arrival in a -second...
Point to Point Ltd provides a service, transporting passengers from Hosea Kutako International Airport to hotels...
Point to Point Ltd provides a service, transporting passengers from Hosea Kutako International Airport to hotels in Windhoek City and the surrounding areas. It enters a contract with Bust Ltd for the lease of five, 25-seater buses for a period of 3 years. The lease payments are constant over the lease term. The market for airport transfer is constantly changing and Point to Point Ltd may need to use similar 25-seater buses or large 40-seater buses, depending on whether other...
Point to Point Ltd provides a service, transporting passengers from Hosea Kutako International Airport to hotels...
Point to Point Ltd provides a service, transporting passengers from Hosea Kutako International Airport to hotels in Windhoek City and the surrounding areas. It enters a contract with Bust Ltd for the lease of five, 25-seater buses for a period of 3 years. The lease payments are constant over the lease term. The market for airport transfer is constantly changing and Point to Point Ltd may need to use similar 25-seater buses or large 40-seater buses, depending on whether other...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT