Let X1, X2, . . . , Xn be a random sample with E(Xk) = 1.5 and Var(Xk) = 9. In addition the sample size is n = 100.
S: sample standard deviation
a) What is the approximate distribution of the sample mean X(X hat)? Justify.
b) Find P(2 < X(X hat) < 3).
c) Assume the sample is normal. Find P(9 < S < 10)
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