Question

What is the probability that exactly 4 customers will arrive in 1 hour, when the mean arrival rate is 3 customers per hour, and interarrival times are exponentially distributed?

a

0.3528

b

0.1847

c

0.1680

d

0.8153

e

0.6472

Answer 1

Mean arrival rate ( $\lambda$ ) = 3 customers per hour

$Prob(X=x) = \frac{\lambda ^{x}* e^{-\lambda }}{x!}$

To find the probability that exactly 4 customers will arrive in 1 hour, we put x = 4 and $\lambda$ = 3 in the above equation.

$Prob(X=4) = \frac{\lambda ^{4}* e^{-\lambda }}{4!}$

= $\frac{3^{4}* e^{-3}}{4*3*2*1}$

= 0.1680

Hence the correct answer is option C.