Question: a) Improperly wired control panels were mistakenly installed on two of eight large automated machine tools. It is uncertain which of the machine tools have

a) Improperly wired control panels were mistakenly installed on two of eight large automated machine tools. It is uncertain which of the machine tools have the defective panels, and a sample of four tools is randomly chosen for inspection. What is the probability that the sample will include no defective panels? Both defective panels?(2+2 = 4 marks)

b) A certain region has an unemployment rate of 6%. The region conducts monthly surveys in order to track the unemployment rate. In a recent month, a random sample of 700 people showed that 35 were unemployed.

(i)Find the probability that the sample unemployment rate is at most 5%.(3 marks)

(ii)Find the probability that the sample proportion will lie within 0.005 of the trueproportionpof people who are unemployed.(3 marks)

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