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.
Answer
 The questioner was satisfied and accepted the answer, or
 The answer was disputed, but the judge evaluated it as 100% correct.
2 Attachments
 answered
 267 views
 $14.76