Question

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?

Answer 1

Answer:

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:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,...$

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)

                    $=1-{4\choose 0}(0.057)^{0}(1-0.057)^{4-0}\\=1-0.7908\\=0.2092$

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