Question: 1.Sampling distribution & middle pack )A random variable has a population mean equal to 526 and population variance equal to 316,027.Your interest lies in estimating

1.Sampling distribution & middle pack)A random variable has apopulation meanequal to 526 andpopulation varianceequal to 316,027.Your interest lies in estimating the population mean of this random variable.With that in mind, you take a representative sample of size 97 from the population of the random variable.You then use this sample data to calculate the sample average as an estimate for the population mean.

(a)Using your knowledge about the central limit theorem (CLT), and assuming that the CLT has already "established itself" / "kicked in" when the sample size is 97, what is the probability that the sample average that you calculated will lie between 483 and 605?

(b)Please calculate the boundaries of the 92% middle pack of the sample average estimator if the sample size had actually been 124.

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