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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)
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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

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