Answer:
0.0821
Step-by-step explanation:
If the arrival rate is 50 customers per hour (60 minutes), then the expected number of customers in 3 minutes is:
[tex]\lambda=\frac{50}{60}*3\\ \lambda=2.5\ customers/3\ minutes[/tex]
Assuming a Poisson distribution with 2.5 customers per 3 minutes, the probability that zero customers arrive for 3 minutes is:
[tex]P(x=k)=\frac{\lambda^k*e^{-\lambda}}{k!}\\P(x=0)=\frac{2.5^0*e^{-2.5}}{0!}\\ P(x=0)=0.0821[/tex]
The probability that the bank stays empty for three minutes is 0.0821.
