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Customers reach the stage of the checkout process in a store, at the following rate: 1...

Customers reach the stage of the checkout process in a store, at the following rate: 1 per hour between midnight and 6 : 00am, 5 per hour between 6 : 00am and 10 : 00am, 10 per hour between 10 : 00am and 4 : 00pm and 6 per hour between 4 : 00pm and midnight. The expected revenue from each such transaction is $5. Suppose that all customers reach the checkout stage finalize their purchase. Please answer all parts of the following question. Please show all work and all steps, and a diagram of this process.

a.) What is the distribution of the number of customers who made a purchase during each calendar day (from midnight until the following midnight)?

b.) What is the probability that no purchase will be made between time 8:00am and 12:00pm?

c.) What is the average revenue of each calendar day?

d.) Suppose that only 50% of the customers reaching the checkout stage actually make a purchase, then what is your answer for the above three questions?

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Answer #1

0 AM - 6iam = (1 per hour) & 6 hours E 6 People 6 AM – 10. Am 2 (5 per hour) x a hours = 20 people lo Am - 4:00 pm - (10 perIf only 50%. People make purchase 0 AM to 6am - (1 per person) & 6hours & 50% - 3 persons Isper prosor) & uhou 10 persons. 10

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