a) A quality inspector draws a simple random sample of 40 bolts from a large shipment and measures the length of each. He finds that 34 of them, or 85%, meet a length specification. He concludes that exactly 85% of the bolts in the shipment meet the specification. The inspector's supervisor concludes that the proportion of good bolts is likely to be close to, but not exactly equal to, 85%. Which conclusion is appropriate?

(CO1: PO1 - 2 marks)

b) Another inspector repeats the study (in Q1a) with a different simple random sample of 40 bolts. She finds that 36 of them, or 90%, are good. The first inspector (in Q1a) claims that she must have done something wrong, since his results showed that 85%, not 90%, of bolts are good. Determine if he is right.

(CO1: PO1 - 2 marks)

c) Customers who purchase a certain make of car can order an engine in any of three sizes. Of all cars sold, 45% have the smallest engine, 35% have the medium-sized one, and 20% have the largest. Among the cars with the smallest engine, 10% fail an emissions test within two years of purchase, while 12% of those with the medium size and 15% of those with the largest engine fail. Calculate the probability that a randomly chosen car will fail an emissions test within two years.

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