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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