Aprocess produces batches of a chemical whose impurity concentrations follow a normal distribution with a variance of175. a random sample of 20 of these batches is chosen. find the probability that the sample variance exceeds 3.10.

Step-by-step explanation:

Previous concepts

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

Data given and notation

For this case we can use the fact that the estimator of the population variance is the sample variance , because

The proof is this one:

Since and

When we take the expected value we got:

We have the distribution on this case given chi square.

Solution to the problem

The degrees of freddom on this case are given by

On this case we want this probability:

And we can use excel to find the probability with the following code:"=1-CHISQ.DIST(33.657,19,TRUE) "

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the answer is d

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step-by-step explanation: