[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]

In an opinion poll it is assumed that an unknown proportion [math]p[/math]

of the people are in favor of a proposed new law and a proportion [math]1-p[/math] are against it. A sample of [math]n[/math] people is taken to obtain their opinion. The proportion [math]{\bar p}[/math] in favor in the sample is taken as an estimate of [math]p[/math]. Using the Central Limit Theorem, determine how large a sample will ensure that the estimate will, with probability .95, be correct to within .01.