A person designing digital art works finds that the time spent on an art work follows Exponential distribution with mean

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A person designing digital art works finds that the time spent
on an art work follows Exponential distribution with mean 20
minutes. If the art works aredesigned in the order in which they
come in and their arrival is approximately follows Poisson
distribution with an average rate of 15 per 8-hour day.
1.What is the probability that the queuing system is empty? (4
marks)
2.What is the probability that the designer is idle? (2
marks)
3.How many hours do the designer idles per day? (2 marks)
4.What is the average length in the queue? (2 marks)
5.On average how many art works are there at the designer in a
day? (2 marks)
6.What is the average waiting time for art works? (2 marks)
7.What is the probability that there are 4 art works to be
designed? (2 marks)
8.What is the probability that there are more than 8 art works
to be designed? (2 marks)
9.What is the waiting time of an art work in the queue? (2
marks)
10.If the arrival rate of art works has doubled per hour, how
many designers are required to provide an equilibrium level of
service? (5 marks)