Conditional upon an unknown scientifific constant, letXifbe iid random variables

representing the future outcomes of a series of experiments, with E(Xi) =units and

Var(Xi) = 400 squared units. The estimator forwill beX=I=1nXi/n . Assuming that the CLT applied with sufficiently fast convergence,

(a) What is the probability that the realization of X will be within 1 unit of

when

i.n= 1?

ii.n= 4?

iii.n= 16?

iv.n= 100?

(b) If the experimenter asks you what is the least number of experiments that

should be performed in order to have a probability of at least 0.95 thatX will be

within 2 units of, what do you reply?