Question: A company has a machine that creates a single type of product. When fully functioning, 4% of the items produced by the machine will be

A company has a machine that creates a single type of product. When fully functioning, 4% of the items produced by the machine will be defective. The company takes a random sample of 7 items produced by the machine. Let the random variable X denote the number of defective items produced by the machine in the sample.

(a) Explain why X could be assumed to follow a Binomial(7,0.04) distribution.

(b) Calculate the probability that no items in the sample are defective.

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