Question

The average number of customers arriving at an ATM machine is 27 per hour during lunch hours. Use equation to denote the number of arrivals in a 5 minute time interval. Assume the customers arrive independently and the number of arrivals within each 5 minutes follows a Poisson distribution. Keep at least 4 decimal digits if the result has more decimal digits. The probability that exactly 2 customers arrive in a given 5 minute interval is closest to

Answer 1

Answer:

The probability that exactly 2 customers arrive in a given 5 minute interval =  0.2667

Step-by-step explanation:

Given -

The average number of customers arriving at an ATM machine is 27 per hour during lunch hours. then the average number of customers arriving at an ATM machine n a 5 minute time interval = $\frac{27}{60} \times 5$ = 2.25

average number of customers arriving at an ATM machine n a 5 minute time interval $(\lambda )$ = 2.25

Let X denote the no of customer arrivals in a 5 minute time interval

The probability that exactly 2 customers arrive in a given 5 minute interval =

P( X = 2 )  = $\frac{e^{-\lambda }\lambda ^{X}}{X!}$            ( Using poision distribution )

               =  $\frac{e^{-2.25} (2.25)^2}{2!}$

               = $\frac{.1054 \times 5.0625}{2}$

               =   0.2667