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larisa86
3 months ago
10

Suppose a shipment of 400 components contains 68 defective and 332 non-defective computer components . From the shipment you tak

e 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?
Mathematics
1 answer:
Leona [12.6K]3 months ago
6 0

Answer:

The calculated standard deviation for the defective components in this sample is 1.88.

Step-by-step explanation:

The sampling is conducted with replacement, indicating that each trial is independent, allowing the use of the binomial probability distribution for this question.

Binomial probability distribution

This calculates the probability of achieving exactly x successes over n independent trials, with p being the success probability.

The expected value for the binomial distribution can be expressed as:

E(X) = np

The standard deviation for the binomial distribution is given by:

\sqrt{V(X)} = \sqrt{np(1-p)}

68 defective parts out of 400:

This indicates that p = \frac{68}{400} = 0.17

From the total shipment, you select a random sample of 25.

<pThis implies that n = 25

Calculating the standard deviation for defective parts in the sample:

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{25*0.17*0.83} = 1.88

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

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