GATE Mechanical Engineering (ME) 2018 Shift 2 Solved Paper

Question : 35 of 65

Marks: +1, -0

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 arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).

Your Answer:

Validate

Solution:

Given, arrival rate,

λ = 30

/hour

λ=\;{1}/{2} {\min}

P= {prob} ⋅=1-e^{-λ t}

P(1)=1-e^{-\;{1}{/}{2} × 1}=0.393

P(3)=1-e^{-λ t}=1-e^{-\;{1}{/}{2} × 3}

=1-e^{-1.5}=0.7768

P(1 ≤ T ≤ 3 {\min})=0.7768-0.393=0.383

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