Special Distributions and Central Limit Theorem.

(a) Suppose Y1, ..., Yn are i.i.d. random variables, each distributed N(10, 4).

Let Y denote the sample mean. Compute P r(9.6 Y 10.4) when n = 1000.

(b) Suppose Y1, ..., Yn are i.i.d. Bernoulli random variables with p = 0.4. Let Y denote the sample mean. Use the central limite theorem to compute approx- imations for P r(Y 0.37) when n = 400.