fExercise 5.35). When a new machine is functioning properly, only 3% of the item

Question

fExercise 5.35). When a new machine is functioning properly, only 3% of the items produced are defective. Assume that we wil randomly select two parts produced on the machine and that we are interested in t number of defective parts found a. Describe the conditions under which this situation would be a binomial experiment. The input in the box below will not be graded, but may be reviewed and considered by your instructor. b, using the Figure 5.3, select a tree diagram that shows this problem as a two-trial experiment. Here D defective: G: not defective. Number ental Number 2nd part Defective st Part 2nd part Defective 1st part CD, G) (G, D) (G,D) G. G) Number Number Defective 2nd part 2nd part 1st part D, D) (G, D)

Explanation / Answer

Solution (a): Since each trial will endup in exactly two outcomes i.e. defective and not defective hence the experiment is binomial experiment with probability of getting defective(success) being 0.003.

Solution (b): Second tree diagram is the correct one as the number of defectives corresponding to all the four possible outcomes is correct.

Solution (c): Since the possible set of outcomes is {(D,D), (D,G), (G,D), (G,G)} , hence the experimental outcomes which will result in exactly one defective is 2.

Solution (d): P{no defective} = P{(G,G)} = 0.25

P{1 defective} = P{(G,D),(D,G)} = 0.5

P{2 defective} = P{(D,D)} = 0.25

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