a company purchases shipments of 600 machine components and uses this acceptance sampling plan: randomly select and test 25 components and accept the whole batch if there are fewer than 3 defective components. it is known that this particular component has a 4% defective rate. what is the probability that shipment will be accepted?

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bammbamm3168 bammbamm3168

21-10-2022
Mathematics

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a company purchases shipments of 600 machine components and uses this acceptance sampling plan: randomly select and test 25 components and accept the whole batch if there are fewer than 3 defective components. it is known that this particular component has a 4% defective rate. what is the probability that shipment will be accepted?

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rafikiedu08 rafikiedu08 · Answer 1 · 2022-10-25T18:03:49+02:00

25 components are randomly chosen and tested; if there are no more than 3 defective components, the entire batch is accepted. The probability is it that the shipment will be accepted is 0.7323.

Given that,

An organization utilizes the following acceptance sampling strategy for ordering shipments of 600 machine parts: 25 components are randomly chosen and tested; if there are no more than 3 defective components, the entire batch is accepted. This specific component is known to have a 4% fault rate.

We have to find how probability is it that the shipment will be accepted.

By binomial we get,

Binomial Problem:

n = 25 ; p = 0.04

P(0<= p <= 2)

= 0.7323

Therefore, The probability is it that the shipment will be accepted is 0.7323.

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