Question: Let X1, X2, . . ., X5 be a random sample from the normal distribution with mean 55 and variance 223. Let and (a) Find

Let X1, X2, . . ., X5 be a random sample from the normal with mean 55 and variance 223. Let

and

(a) Find the distribution of the random variables Y and Z.
(b) Are Y and Z independent?
(c) Find
(i) P(0.62 ‰¤ Y ‰¤ 0.76), and
(ii) P (0.77 ‰¤ Z ‰¤ 0.95).

Y ( X,-55) 2/223 z- (x,-M2/223. 1

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