Question

The arrival of customers over fixed time intervals in a bank follow a poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrival is between 1 and 3 m minutes is (correct to two decimal places).

• A. 0.38

Answer 1

The correct option is A 0.38

Average no. of customers $=30/hr=0.5/min=\mu$

Poisson distribution function is $f\left(t\right)=\mu e^{-\mu t}$
$[\because$ Inter arrival time follow) Exponential distribution]

$\text{and}P(0<t<t_1)$

$={\int }_0^{t_1}f\left(t\right)dt=1-e^{-\mu t_1}$

$\text{so,}P(0\le t\le 1)=1-e^{-\mu \left(1\right)}=1-e^{-1/2}=0.393\text{and}P(0\le t\le 3)$

$=1-e^{-3\mu }=1-e^{-\frac{3}{2}}=0.7768$

so, P(successive customer arrival between 1 to 3 min)

$=P(1\le t\le 3)=0.7768-0.398=0.38$