In order to find out the probability that a student will bring a car to campus, $100$ students are polled. Of those students, $85$ have cars to bring to campus.

$1.$Find a point estimate for the proportion of students who will bring a car to campus.

$2.$ Is it appropriate to use a normal distribution to approximate the p distribution?

No$,$ even though np $>5,$ we have that nq $<5.$

No$,$ even though nq $>5,$ we have that np $<5.$

No$,$ both np $<5$ and nq $<5.$

Yes, both np $>5$ and nq $>5.$

$3.$For the $95\%$ confidence level, find zc$,$ the critical value for the given confidence level

$4.$For the $95\%$ confidence level, find the error, E$,$ for the confidence interval $($round your answer to two decimal places$).$

$5.$Find the $95\%$ confidence interval for the proportion of students who bring their car on campus.

$6.$The study that was done was a preliminary study and the school will need to repeat the poll to get a $95\%$ confidence interval. What should be the sample size in order for the error to be less than $\mathrm{.}08?$