The population proportion is $0\mathrm{.}20.$ What is the probability that a sample proportion will be within $+-0\mathrm{.}05$ of the population proportion for each of the following sample sizes? Round your answers to $4$ decimal places. Use $z-$table.

a$.n=100$

b$.n=200$

c$.n=500$

d$.n=1000$

e$.$ What is the advantage of a larger sample size?

With a larger sample, there is a probability $\frac{?}{\text{b}\text{a}\text{r}}(p)$ will be within $+-0\mathrm{.}05$ of the population proportion $p.$