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)

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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.