Mathematics: Consider a manufacturing process with a quality inspection station. in the past, 15% of parts are defective. as soon as one defective part is found, the process is stopped. if 8 parts have been inspected without finding a defective part, what is the probability that at least 11 total parts will be inspected before the process is stopped?

x-6Step-by-step explanation:...

Consider a manufacturing process with a quality inspection

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13.01.2022

0.614125

Step-by-step explanation:

Given that a manufacturing process with a quality inspection station has on an average 15% of parts are defective.

As soon as one defective part is found, the process is stopped.

We find that number of defectives would be binomial because each part randomly selected has a constant probability of 0.15 being defective

Probability that at least 11 total parts will be inspected before the process is stopped/8 parts have been inspected without finding a defective part

= $P(x\geq 11)/P(x=8)\\$

= Probability of 9th, 10th, 11th should not be defective

= $(1-0.15)^3\\= 0.614125$

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