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This question is a hybrid question.  Please clearly label a blank piece of paper with this question number and write your response to this question.

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 This question is worth 8 marks.

An apple orchard processes apples into juice during harvest season. The volume of juice processed each day, in ML (megalitres), is a random variable with a probability density function given by:

 

If  

a)  What is the exact probability that on a randomly chosen day, less than 1.2 ML of juice is processed ?  Show all working.                  [2 marks]

b)  What is the average volume of juice, , processed daily? Give your answer in exact form.    [3 marks]

c) On 50% of the days, at least ML of juice is processed.  Find the value of , correct to 2 decimal places.    [3 marks]

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