ABC Manufacturing has a policy that it will reject a shipment of parts from its supplier if inspectors find any defective parts in a random sample of 4 parts from the shipment. The supplier has been in business many years and has a long-term defective rate for parts of 5.7%. What is the probability that a shipment will be rejected after a given sample of parts is checked?

The probability that a shipment will be rejected after a given sample of parts is checked is 0.2092.

Step-by-step explanation:

Let X = number of defective parts in the sample.

The proportion of defective parts produced by the supplier is, P (X) = p = 0.057.

The sample selected by the inspector is of size , n = 4.

A particular being defective is independent of any other part being defective.

Thus, the distribution of the random variable X is Binomial.

The probability function of the Binomial distribution is:

The policy of the manufacturing company states that it will reject a shipment of parts from its supplier if inspectors find any defective parts in a random sample of 4 parts from the shipment.

The probability of a shipment being rejected is,

P (Rejected) = 1 - P (Accepted)

                    = 1 - P (X = 0)

Thus, the probability that a shipment will be rejected after a given sample of parts is checked is 0.2092.

step-by-step explanation:

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