When a new machine is functioning properly, only 3% of the items produced are defective. Assume that we randomly select 100 parts produced and we are interested in the number of defective parts found. a) What is the probability that at least one defective part will be found? b) How many defective parts do you expect to find in a sample of size 100? c) What is the standard deviation of the number of defective parts? d) What is the probability that the number of defective parts will exceed the mean by two standard deviations? (Hint: find P(X ≥ µ+20))

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