[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Let [math]S_n[/math] be the number of successes in [math]n[/math] Bernoulli trials with

probability .8 for success on each trial. Let [math]A_n = S_n/n[/math] be the average number of successes. In each case give the value for the limit, and give a reason for your answer.

• [math]\lim_{n \to \infty} P(A_n = .8)[/math].
• [math]\lim_{n \to \infty} P(.7n \lt S_n \lt .9n)[/math].
• [math]\lim_{n \to \infty} P(S_n \lt .8n + .8\sqrt n)[/math].
• [math]\lim_{n \to \infty} P(.79 \lt A_n \lt .81)[/math].