Suppose that we have disjoint normal populations A and B with equal population variances.   Suppose we plan a sample of size 4 from from population A and a sample of size 9 from population B which we will pool to form the pooled variance.  If you know the population variances are both in fact equal to 6, what is the probability that the pooled variance of the two samples will turn out to be less than 8 given your information?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Suppose that we have disjoint normal populations A and B with equal population variances.   Suppose we plan a sample of size 4 from from population A and a sample of size 9 from population B which we will pool to form the pooled variance.  If you know the population variances are both in fact equal to 6, what is the probability that the pooled variance of the two samples will turn out to be less than 8 given your information?

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