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A random sample X1,...,X300 is drawn from a population with a mean µ = 80 and...

A random sample X1,...,X300 is drawn from a population with a mean µ = 80 and standard deviation σ = 30 but unknown distribution. Let U = (X1 + ...+X100)/100 represent the sample mean of the first 100 observations and V = (X100 + ...+X300)/200 represent the sample mean of the last 200 observations. a[10 points] What are the approximate distributions of U and V ? b[10 points] Which probability would you expect to be larger, P(70 <= U <= 90) or P(70 <= U <= 90)?

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