Let ${Y}_i$ be i.i.d random variables with i= 1,...,n each normally distributed at N(10,4).
a. Solve for P(9.6 ≤ $\bar{Y}$ ≤ 10.4) when the sample size equals i.) n=20 ii.) n=100 iii.) n=1000
b.Let c be a positive number. Show that P( 10-c ≤ $\bar{Y}$ ≤ 10+c) approaches 1 as n grows large.
c. Use (b) to show that the probability limit of $\bar{Y}$ is 10.
I already answered a.i. and a.ii. How should I go about the remaining items? Thanks!