Suppose a shipment of 400 components contains 68 defective and 332 non-defective computer components . From the shipment you take a random sample of 25. When sampling with replacement (so that the p = probability of success does not change), note that a success in this case is selecting a defective part. The standard deviation of this situation is?

The standard deviation for the number of defective parts in the sample is 1.88.

Step-by-step explanation:

The sample is with replacement, which means that the trials are independent, and thus, the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.  

The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

68 defective out of 400:

This means that

From the shipment you take a random sample of 25.

This means that

Standard deviation for the number of defective parts in the sample:

The standard deviation for the number of defective parts in the sample is 1.88.

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step-by-step explanation: