Suppose Yi = 1, 2, . . . , n, are i.i.d. random variables, each distributed N(10,

Question:

Suppose Yi = 1, 2, . . . , n, are i.i.d. random variables, each distributed N(10, 4).
(a) Compute Pr(9.6 ≤ ≤ 10.4) when (i) n = 20, (ii) n = 100, and (iii) n = 100f).
(b) Suppose c is a positive number. Show that Pr(10 - c ≤ ≤ 10 + c) becomes close to 1.0 as n grows large.
(c) Use your answer in (b) to argue that converges in probability to 10.