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  3. question 2 a department manager is considering purchasing a new...

Question: question 2 a department manager is considering purchasing a new...

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Question 2 A department manager is considering purchasing a new photocopy machine. One consideration is how often the machine will need repairs. Let X denote the number of repairs during a year. Based on past experience, X has the following PMF (a) Px(x) 0.4 0,3 0.2 x, # repairs i) What is the expected number of repairs during a year? ii) What are its variance and standard deviation? [7 marks (b) The probability that Trevor eats breakfast and gets to work on time is 0.2. The probability that he eats breakfast is 0.4. If Trevor eats breakfast, what is the probability that he is on time for work? [4 marks (c) A company produces toy robots. A microchip inside the robot controls all its actions. The company buys 30% of its required microchips from Supplier 1, and the remainder from Supplier 2, Supplier l has a record of providing microchips with 8% defectives. Supplier 2 has a defective rate of 5%. The company does not have any testing procedures in place to find the defective chips. i) Suppose you pick a robot randomly from the production line. What is the probability that it has a defective microchip? ii)If a randomly selected robot malfunctions because of its defective microchip, what is the probability that supplier 2 has provided the corresponding microchip? 9 marks]

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