A company purchases shipments of machine components and uses this acceptance 11) sampling plan: Randomly select and test 30 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 6 % rate of defects, what is the probability that this whole shipment will be accepted?

Probability that this whole shipment will be accepted is 0.7324.

Step-by-step explanation:

We are given that a company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 30 components and accept the whole batch if there are fewer than 3 defectives.

The above situation can be represented through Binomial distribution;

where, n = number of trials (samples) taken = 30 components

            r = number of success = fewer than 3

           p = probability of success which in our question is % rate

                 of defects, i.e; 6%

LET X = Number of defective components

So, it means X ~

Now, Probability that this whole shipment will be accepted only when there are fewer than 3 defectives = P(X < 3)

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

=

=

= 0.7324

Therefore, probability that this whole shipment will be accepted is 0.7324.