# Exam P Practice Problem 19 – Poisson Streams of Customers

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Problem 19A

The customers at a gift shop can be classified into one of three distinct types – type 1 (customers making no purchase), type 2 (customers making purchases each of which is under $20) and type 3 (customers making purchases each of which is$20 or over). Assume that the arrivals of the three types of customers are independent. The number of customers arriving at this gift shop follows a Poisson distribution with a mean of 12 per hour (type 1), with a mean of 24 per hour (type 2) and with a mean of 6 per hour (type 3). What is the probability that more than 5 customers will arrive in a 10-minute period?

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Problem 19B
The number of male customers arriving at a women clothing store follows a Poisson distribution with a mean of 5 per hour. The number of female customers arriving at a women clothing store follows a Poisson distribution with a mean of 20 per hour. Assume that the arrivals of male and female customers are independent. What is the probability that the number of customers arriving at this women clothing store in a 15-minute period exceeds what is expected in a 15-minute period?

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