A random sample of 12 observations is takenfrom a normal population having the v

Question

A random sample of 12 observations is takenfrom a normal population having the variance 42.5. Find theapproximate probability of obtaining a sample standard deviationbetween 4.23 and 9.21. A random sample of 12 observations is takenfrom a normal population having the variance 42.5. Find theapproximate probability of obtaining a sample standard deviationbetween 4.23 and 9.21. A random sample of 12 observations is takenfrom a normal population having the variance 42.5. Find theapproximate probability of obtaining a sample standard deviationbetween 4.23 and 9.21.

Explanation / Answer

Since twelve observations are from a normal distribution with2=42.5 we know
X2=(n-1)s2/2 is distributed as a chi-square with n-1 degrees offreedom. Thus the probability of a sample standard deviationfalling between 4.23 and 9.21 is given by P{11(4.23)2/42.5<X2<11(9.21)2/42.5}=.923

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