SOLUTION: d) The arrival rate of customers arriving at a bank counter follows a Poisson distribution with a mean rate of 4 per 10 minutes interval. Find the probability that
i. Exactly 0
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Question 1166273: d) The arrival rate of customers arriving at a bank counter follows a Poisson distribution with a mean rate of 4 per 10 minutes interval. Find the probability that
i. Exactly 0 customer will arrive in 10 minutes interval
ii. Exactly 2 customers will arrive in 10 minutes interval
iii. At most 2 customers will arrive in 10 minutes interval
iv. At least 3 customers will arrive in 10 minutes interval
(e) In a mainframe computer centre, execution time of programs follows an exponential distribution. The average execution time of the programs is 5 minutes. Find the probability that the execution time of programs is:
i. Less than 4 minutes
ii. More than 6 minutes
Answer by themasterofcircuits(27) (Show Source): You can put this solution on YOUR website!
d.)
The Poisson distribution is as follows:
Here, u is the mean, or 4 in this case.
i.) = 0.01832
ii.) = 0.14653
iii.) =
= 0.01832
= 0.07326
= 0.14653
= 0.01832+0.07326+0.14653 = 0.23811
iv.)
= 1-0.23811=0.76819
e.) I have done d.) for you. e.) is the same idea, except you need to use the Exponential Distribution, which is a special case of the Poisson Distribution.
The exponential distribution is given by:
The letter cutoff in the exponential is an 'x'.
Good luck!
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