1. A manufacturer of metal pistons finds that on the average, 12% of his pistons arerejected because they are either oversize or undersize. What is the probability that abatchof10pistonswill contain: (Express youranswerscorrectto4 decimalplaces):

1. Atleast2rejects? [3 marks]

1. Exactly3rejects? [2 marks]

1. Findthemean [1 mark]

1. Consider the experiment of flipping a coin three times. You then count the number ofheads.(Forquestionsc)andd)express youranswercorrectto2decimalplaces.)
2. Statetherandomvariableandcreatethesamplespace[1mark]
3. Createatableshowingtheprobabilitydistributionforthenumberofheads.[2marks]
4. Findthemeannumberofheads.[2marks]
5. Findthestandarddeviationforthenumberofheads.[2marks]

1. Find the following probabilities. For full marks, provide a graph showing thecorrespondingarea: [6marks]

a)P (0<<2.34)

b)P(>1.57)

c) P(1.34<<1.23)

1. Findthevalue(score)thatseparatesthetop15%ofthedatafromthebottom85%ofthe data for a normal distribution with a mean of 56 min and a standard deviation of 9min.Express your answer correctto1 decimal place.

[4marks]

1. Find the 38thpercentile for a normal distribution with a mean of 15.6 lbs and astandarddeviationof2.5 lbs.Expressyouranswercorrectto1decimalplace.