The proportion of individuals insured by the All$-$Driver Automobile Insurance Company who received at least one traffic ticket during a five$-$year period is $0\mathrm{.}15.$ Use the $z-$table.

a$.$ Show the sampling distribution of $\frac{?}{\text{b}\text{a}\text{r}}(p)$ if a random sample of $150$ insured individuals is used to estimate the proportion having received at least one ticket.

$E(\frac{?}{\text{b}\text{a}\text{r}}(p))=$

$(to2$ decimals$)$

${}_{\frac{?}{\text{b}\text{a}\text{r}}(p)}=$

$(to4$ decimals$)$

Can the sampling distribution of $\frac{?}{\text{b}\text{a}\text{r}}(p)$ be approximated by a normal distribution?

b$.$ What is the probability that the sample proportion will be within $+-0\mathrm{.}03$ of the population proportion $($to $4$ decimals$)?$ Round $z-$value to $2$ decimals.