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Answer:
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.