On average, there are 10 customers arrives a local bank per hour. Bob is the only bank teller on duty at the bank currently and needs to run out for 6 minutes. What is the probability that no customer will arrive in the next 6 minutes?

the probability that no customer will arrive in the next 6 minutes = 0.36788 = 0.368

Step-by-step explanation:

If there are 10 customers per hour, this translates to 1 customer per 6 minutes

So, if there's a mean of 1 customer per 6 minutes, to obtain the probability that no customer will come in a 6 minute interval, this becomes a Poisson distribution problem.

The Poisson distribution formula is given by

P (X = x) = (e^-λ) (λˣ) / x!

where λ = mean = 1 customer per 6 minutes

x = 0 customer per 6 minutes

P (X=0) = (e⁻¹) (1⁰) / 0! = 0.36788 = 0.368