Question

An analyst in Bank of America, Santa Clara University Branch, believes that on Mondays customers arrive at the bank with rate 50 customers per hour. What is the probability that, during this period, the bank becomes empty for 3 minutes

Answer 1

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:

$\lambda=\frac{50}{60}*3\\ \lambda=2.5\ customers/3\ minutes$

Assuming a Poisson distribution with 2.5 customers per 3 minutes, the probability that zero customers arrive for 3 minutes is:

$P(x=k)=\frac{\lambda^k*e^{-\lambda}}{k!}\\P(x=0)=\frac{2.5^0*e^{-2.5}}{0!}\\ P(x=0)=0.0821$

The probability that the bank stays empty for three minutes is 0.0821.