1. An unbalanced die was rolled 5000 times; that is, the sample of outcomes s was generated via s ← RE₁ (5000), where RE₁ = "roll the die once." Let X = "number of up-dots." It turned out that the sample mean was x = mean (X:s) = 3.08 and the sample standard deviation was s = sd(X:s) = 1.55. In addition, 1200 (or 24%) of the 5000 rolls resulted in more than 4 up-dots; i.e., ô(s) = prop(X > 4) = 0.24. (a) By what fundamental result can we expect the sample distribution dist(X:s) to be close to the process distribution dist (X: RE₁)? (b) By what fundamental result can we expect mean(X:s) to be close to mean(X: RE₁) and prop(X > 4) to be close to PRE₂ (X > 4)? (c) What is your best guess at (d) What is your best guess at sd(X: RE₁) and why? PRE₁ (X ≤ 4) and why?

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1. An unbalanced die was rolled 5000 times; that is, the sample of outcomes s was generated via s ← RE₁ (5000),
where RE₁ "roll the die once." Let X = "number of up-dots." It turned out that the sample mean was x =
mean(X:s) = 3.08 and the sample standard deviation was s = sd (X:s) = 1.55. In addition, 1200 (or 24%) of the
5000 rolls resulted in more than 4 up-dots; i.e., ô(s) = prop§(X > 4) = 0.24.
(a) By what fundamental result can we expect the sample distribution dist(X:s) to be close to the process distribution
dist (X: RE₁)?
(b) By what fundamental result can we expect mean(X:s) to be close to mean(X: RE₁) and prop(X > 4) to be close
to PRE₁ (X > 4)?
(c) What is your best guess at sd(X: RE₁) and why?
(d) What is your best guess at PRE₁ (X ≤ 4) and why?
Transcribed Image Text:1. An unbalanced die was rolled 5000 times; that is, the sample of outcomes s was generated via s ← RE₁ (5000), where RE₁ "roll the die once." Let X = "number of up-dots." It turned out that the sample mean was x = mean(X:s) = 3.08 and the sample standard deviation was s = sd (X:s) = 1.55. In addition, 1200 (or 24%) of the 5000 rolls resulted in more than 4 up-dots; i.e., ô(s) = prop§(X > 4) = 0.24. (a) By what fundamental result can we expect the sample distribution dist(X:s) to be close to the process distribution dist (X: RE₁)? (b) By what fundamental result can we expect mean(X:s) to be close to mean(X: RE₁) and prop(X > 4) to be close to PRE₁ (X > 4)? (c) What is your best guess at sd(X: RE₁) and why? (d) What is your best guess at PRE₁ (X ≤ 4) and why?
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