GATE2018-2-24

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 $3$ minutes is _____ (correct to two decimal places)

Answer 1

λ = 30 customers/hour

==> 30/60 customers/minute

==> 0.5 customers/minute

P(a<=X<=b) = e^-λa - e^-λb 

P(1<=X<=3) = e^-0.5*1 - e^-0.5*3 

P(1<=X<=3) = e^-0.5 - e^-1.5 = 0.6065 - 0.2231 = 0.3834

Comments

Isn't the formula e^(-mean) * (mean^t)/fact(t) for Poisson distribution then why are we using        e^(-mean*t) formula