Question: Let X1,X2,...,X12 be independent and identically distributed continuous random variables. For k = 1,2,...,12: (a) If E[Xk] = 110 and Xk 0, what can be

Let X1,X2,...,X12 be independent and identically distributed continuous random variables. For k = 1,2,...,12:

(a) If E[Xk] = 110 and Xk 0, what can be said about P(Xk 120)?

(b) If in addition to the mean above, you know thatVar(Xk) = 50, what can be said about P(85 < X < 135)?

(c) Let X = X1 +X2 ++X12. Using the mean and variance above, approximate P(X > 1270).

Write your answer in terms of (z) with z 0, the cdf of the standard normal random variable.

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