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Question 3a                                       (3 + 3 = 6 marks)

 

i)           At a recent election, 30% of voters in a certain electorate gave their first preference to the Greens candidate. If 15 people on the electoral roll for the electorate were randomly selected, find the probability that between 3 and 6 voters inclusive, gave their first preference to the Green candidate.

 

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ii)          Based on past experience, it is assumed that the number of flaws per metre in rolls of grade 2 paper follow a Poisson distribution with a mean of one flaws per 20 metres of paper. What is the probability that in a 10-metre       roll there will be at least one flaw?

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Question 3b                                       (2 + 2 + 3 = 7 marks)

 

A local shopping centre pays its employees a mean hourly wage of $7.25 with a standard deviation of $0.60. It is known that the hourly wage is normally distributed and paid to the nearest cent.

 

i).          What is the probability that a randomly selected employee receives an hourly wage of less than $6?

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ii).         The highest 1% of employee’s hourly wages exceeds what amount?

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iii)         What is the probability that the average hourly wage from a sample of 9 employees exceeds $7.80?

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