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) About Me  (Show Source):
You can put this solution on YOUR website!
d.)
The Poisson distribution is as follows: P%28x%2Cu%29=%28e%5E%28-u%29%2Au%5Ex%29%2Fx%21
Here, u is the mean, or 4 in this case.
i.) P%280%2C4%29=%28e%5E%28-4%29%2A4%5E0%29%2F0%21 = 0.01832

ii.) P%282%2C4%29=%28e%5E%28-4%29%2A4%5E2%29%2F2%21 = 0.14653

iii.) P%28x%3C=2%29=P%28x=0%29%2BP%28x=1%29%2BP%28x=2%29 = P%280%2C4%29%2BP%281%2C4%29%2BP%282%2C4%29
P%280%2C4%29=%28e%5E%28-4%29%2A4%5E0%29%2F0%21 = 0.01832
P%281%2C4%29=%28e%5E%28-4%29%2A4%5E1%29%2F1%21 = 0.07326
P%282%2C4%29=%28e%5E%28-4%29%2A4%5E2%29%2F2%21 = 0.14653
P%28x%3C=2%29 = 0.01832+0.07326+0.14653 = 0.23811

iv.) P%28x%3E=3%29=1-P%28x%3C3%29=1-P%28x%3C=2%29
1-P%28x%3C=2%29 = 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: P%28x%2Cu%29=%281%2Fu%29%2Ae%5E%28-x%2Fu%29
The letter cutoff in the exponential is an 'x'.
Good luck!