GATE ME 2021 Set 1 — Question 43
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Engineering Mathematics → Statistics & Distributions → Poisson Distribution
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Question
Customers arrive at a shop according to the Poisson distribution with a mean of 10 customers/hour. The manager notes that no customer arrives for the first 3 minutes after the shop opens. The probability that a customer arrives within the next 3 minutes is
Correct answer
(A) 0.39
Solution
The Poisson process is memoryless. The probability of an arrival in the next 3 minutes is independent of what happened in the previous 3 minutes. The arrival rate is . For a time interval , the mean number of arrivals is . The probability of at least one arrival is . Rounding to two decimal places gives 0.39.
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