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s230.as2.F09 - that is not in stock during a 75-minute...

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Probability Statistics 230, Fall 2009 Assignment 2 (Be sure to print your name and ID number on your assignment) 1. A merchant finds that 10% of customers ask for an item which is not in stock. Customers arrive according to the conditions for a Poisson process with an average rate of 12 per hour. (a) In this context, state the conditions for a Poisson process. (b) Find the probability of 4 customers arriving in a 10-minute period. (c) Find the probability 2 customers ask for an item that is not in stock, out of 20 customers at the store. (d) Find the probability the x th customer arriving at the store is the 3 rd to ask for an item which is not in stock. (e) Give an expression for the probability that 3 customers will ask for an item
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Unformatted text preview: that is not in stock during a 75-minute period. 2. A doctor can diagnose H1N1 flu in 70% of patients who have the virus simply from a description of the symptoms. The doctor also diagnoses H1N1 in 10% of people with non-H1N1 flu, based on symptoms. The doctor charges $100 for a diagnosis. Each flu patient diagnosed by the doctor as having the H1N1 virus is given a follow-up blood test at a cost of $300. The blood test always gives correct conclusions. Suppose 1000 people with flu go to their doctors for an H1N1 diagnosis and each has a 40% chance their flu is H1N1. Find the expectation of (a) the number of H1N1 flu cases detected by the above process. (b) the total cost of all diagnoses....
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