1. An unbalanced die was rolled 5000 times; that is, the sample of outcomes s was...

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1. An unbalanced die was rolled 5000 times; that is, the sample of outcomes s was generated via s- RE, (5000), where RE, "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., p(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: RE,)? (b) By what fundamental result can we expect mean(X:s) to be close to mean(X: RE,) and prop, (X > 4) to be close to PRE, (X > 4)? (c) What is your best guess at sd(X: RE₂) and why? (d) What is your best guess at PRE, (XS4) and why? 1. An unbalanced die was rolled 5000 times; that is, the sample of outcomes s was generated via s- RE, (5000), where RE, "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., p(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: RE,)? (b) By what fundamental result can we expect mean(X:s) to be close to mean(X: RE,) and prop, (X > 4) to be close to PRE, (X > 4)? (c) What is your best guess at sd(X: RE₂) and why? (d) What is your best guess at PRE, (XS4) and why?

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a By the law of large numbers The law of large numbers states that as the sample size increases the ... View the full answer