Let X1, X2, . . ., X5 be a random sample from the normal distribution with mean

Question:

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).

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...