Question: A2. A company has a machine that creates a single type of product. When fully functioning, 3% of the items produced by the machine are

A2. A company has a machine that creates a single type of product. When fully functioning, 3% of the items produced by the machine are defective, 87% are of normal grade and 10% are of superior grade. The company takes a random sample of 10 items produced by the machine. Let the random variable X denote the number of superior grade items produced by the machine in the sample.

(a) Explain why X could be assumed to follow a Binomial(10,0.1) distribution.

(b) Calculate the probability that no items in the sample are of superior grade.

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