# Probability and Statistics problem

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)

• Bounty is too low

• How much do you think is reasonable?

• S is never defined

• I guess, it is the probability of a random sample being between 9 and 10?

• That doesn’t make sense. Find out what S means and then come back

• just updated. s is now defined

• Are you sure It's not supposed to be S^2, the sample variance? Or maybe the Variance of Xk is supposed to be 9^2 not 9? As written, the answer to c is pretty much 0, so I think there might be a typo.

• Yep. This is an exact copy from my assignment and my professor said that there are no typos.

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