Fred owns a company that produces thousands of pegs each day. He randomly selects 41 pegs that are produced on one day and finds eight faulty pegs.

1. What is the proportion of faulty pegs in this sample?  (1 mark) 
   

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2. Pegs are packed each day in boxes. Each box holds 12 pegs. Let    be the random variable that represents the proportion of faulty pegs in a box.
3. The actual proportion of faulty pegs produced by the company each day is .
4. Find  . Express your answer in the form  , where    and    are positive rational numbers and    is a positive integer.  (2 marks)
   

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