The number of people who use the ATM at night outside your local bank branch can be modeled as a Poisson distribution. On average 1.2 customers arrive every hour (late at night). You park outside the bank to count the customers. What is the probability that in the hour between 10 and 11 PM at most 3 customers arrive?

Accepted Solution

Step-by-step explanation:First we have to remember the Poisson distribution equation which is:[tex]\frac{L^{r} }{r!} *e^{-r}[/tex]Where L is defined by the mean in this case is 1.2And r is the number of occurrences, in this case is 0,1,2,3 because we want to know the probability that at most 3 costumers arrive in one hourNow we apply the formula with the given data and we will obtain [tex]e^{-1.2}=0.30119[/tex][tex]{1.2^{} Β *e^{-1.2}=0.3614[/tex][tex]\frac{1.2^{2} }{2!} *e^{-1.2}=0.21686[/tex][tex]\frac{1.2^{3} }{3!} *e^{-1.2}=0.08674[/tex]