Here is an example where it is plausible to know the

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Unformatted text preview: this chapter, we will assume the knowledge of µ and σ 2 of the population and figure out the distribution of x . ¯ Statistics is about estimation population parameters, so usually we don’t know µ or σ 2 . We are mostly building up our arsenal for the next chapters. Here is an example where it is plausible to know the population parameters: Suppose we have a random sample of 100 Michigan students and we observe their GPA’s. It is known that in the population (university) average GPA is 3 and standard deviation of GPA is 0.4. What is the probability of a randomly picked student having a GPA above 3.1 Can you figure this out? NO, without further info about the population distribution of GPA’s. I did not tell you what distribution population has. Utku Suleymanoglu (UMich) Sampling Distributions 15 / 21 Sampling Distributions But you can figure out the probability of the sample mean of 100 students’ GPA’s exceeding 3.1! What is the sampling mean and the variance of x ? ¯ √ ¯ E (X ) = µ = 3, V (X )...
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