A bank manager wishes to provide prompt service for customers at the bank's drive-up window. the bank currently can serve up to 10 customers per 15-minute period without significant delay. the average arrival rate is 7 customers per 15-minute period. let x denote the number of customers arriving per 15-minute period. assuming x has a poisson distribution: (a) find the probability that 10 customers will arrive in a particular 15-minute period. (round your answer to 4 decimal places.) probability (b) find the probability that 10 or fewer customers will arrive in a particular 15-minute period. (do not round intermediate calculations for calculating probability. round your answer to 4 decimal places.) probability (c) find the probability that there will be a significant delay at the drive-up window. that is, find the probability that more than 10 customers will arrive during a particular 15-minute period. (do not round intermediate calculations for calculating probability. round your answer to 4 decimal places.) probability
The Poisson distribution with mean λ has [tex]P(K=k)=\frac{\lambda ^k e^{-\lambda}}{k!}[/tex]
Here time period = 15 minutes λ =7
(a) k=10 customers arrive within a time period (15 minutes) Find P(K=10) [tex]P(K=k)=\frac{\lambda ^k e^{-\lambda}}{k!}[/tex] [tex]=\frac{7 ^{10} e^{-7}}{10!}[/tex] [tex]=0.0709833[/tex]
