The arrival rate of customers at a service window of a cinema hall follows a probability distribution with a mean rate of 45 per hour. If the service rate of the clerk follows poisson distribution, with a mean of 60 per hours, what is the probability of having no customer in the system?

The arrival rate of customers at a service window of a cinema hall follows a probability distribution with a mean rate of 45 per hour. If the service rate of the clerk follows poisson distribution, with a mean of 60 per hours, what is the probability of having no customer in the system? Correct Answer 0.25

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Related Questions

S1: A man handed a pair of trousers to the departmental store-clerk and said,"I'd like these altered, please".
P: He said that free alteration is not possible without a receipt.
Q: The man said,"Okay, I'd like to return the trousers". The clerk took them back and returned his money.
R: The man pushed the money and said,"Now I want to buy them". The clerk put the trousers in a bag, issued receipt and handed him both.
S: The clerk asked for the sales receipt but after searching his pockets the man replied that he had lost it.
S6: Triumphantly he put the trousers and the receipt on the counter and said,'I'd like to have these altered, please."

The Proper sequence should be:
Directions : In each of the following questions a statement is given, followed by three conclusions. Give answer :

Statement : Give this packet to Mr. X at his residence and return immediately. In case you are likely to be late inform me - Mr. A tells his clerk.

Assumptions :
I. The clerk never informs about his late coming.
II. The clerk may not obey Mr. X instructions.
III. The clerk may not inform his late coming unless instructed.
In an opencast mine, dumpers arrive at a shovel location with an average arrival rate of 12 per/hour. The inter-arrival times of the dumpers follow an exponential distribution. The service times of the shovel also follow an exponential distribution with an average of 3 minute. The average waiting time of a dumper in the queue in minutes is
A pipe, working at full speed, can fill an empty cistern in 1 hour. However, during the first hour it worked at one-twelfth of its capacity, during the second hour at one-ninth of its capacity, during the third hour at one-sixth of its usual capacity and during the fifth hour it was only one -third as efficient as it was supposed to be. A second pipe also displayed similar performance, but if it worked at full speed would have filled the empty cistern in 2 hours. Together with a drain pipe that drained water out of the tank at a constant rate, the empty cistern could be filled in 5 hours, all the three pipes working concurrently. How many hours will it take the drain pipe to empty the filled cistern if no other pipe was functioning during the time?
Statement : The cinema halls are incurring heavy losses these days as people prefer to watch movies in home on TV than to visit cinema halls.

Courses of Action :
I. The cinema halls should be demolished and residential multi-storey buildings should be constructed there.
II. The cinema halls should be converted into shopping malls.
S1: Go to the library and see the clerk.
P: When you have chosen the books you wish to take home, you take them to the clerk with the tickets.
Q: You will probably have to sign a form promising to take care of the books.
R: Then you are usually given two or three ticket with your name and address on them.
S: The clerk keeps the tickets until you return the books.
S6: He stamps the books with a date.

The Proper sequence should be:
In an opencast mine loading and transporting has been carried out by shovel dumper combination. There is only one shovel is in operation. Dumpers arrive at the rate of 10 dumpers per hour and it takes shovel on an average 5 minutes to load a dumper. Assume arrival is Poisson and service time is exponentially distributed. Find the probability that the shovel is sitting idle.
A business firm reduces the number of hours its emplyess work from 40 hours per week to 36 hours per week while continuing to pay the same amount of money. If an employee earned x taka per hour before the reduction in hours, how much does he earn per hour under the new system?
In an opencast mine loading and transporting has been carried out by shovel dumper combination. There is only one shovel is in operation. Dumpers arrive at the rate of 10 dumpers per hour and it takes shovel on an average 5 minutes to load a dumper. Assume arrival is Poisson and service time is exponentially distributed. What is expected idle time of a dumper in the system?
In an opencast mine loading and transporting has been carried out by shovel dumper combination. There is only one shovel is in operation. Dumpers arrive at the rate of 10 dumpers per hour and it takes shovel on an average 5 minutes to load a dumper. Assume arrival is Poisson and service time is exponentially distributed. Find the expected number of dumpers in the system.