A random sample x1, ....., x150 is drawn from a population with mean ??=40 and standard deviation ??=15 but an unknown distribution. Let U=(X1+......+X50)/50 represent the sample mean of the first 50 observations and V=(X51+.....+X150)/100 the sample mean of the last 100 observations a) what are the approximate distributions of U and V? b) Which probability would you expect to be larger, P(35<=U<=45) or P(35<=V<=45)? why? c) Find P(35<=U<=45) and P(35<=V<=45) using the normal approximation.