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Arrivals at a walk-in optometry department in a shopping centre have been found to be Poisson...

Arrivals at a walk-in optometry department in a shopping centre have been found to be Poisson distributed with a mean of 2.71 potential customers arriving per hour. Assuming that the Poisson distribution is reasonable for this situation, where X is the number of arrivals during a given hour. Calculate the probability of at least 19 customers between 2pm and 6pm? Give the answer to the two decimal places.

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Answer #1

Let y denote the number of walk-in in the centre per 4 hours. Then

Using Normal approximation to Poission, we have,

Required probability =

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