8. Sampling Distributions & Confidence Intervals: Proportion

Over the first $20$ days of the semester, one student is late to class on $6$ days. Find the margin of error for a $98\%$ confidence interval for the true proportion of time this student is late.

Over the first $20$ days of the semester, one student is late to class on $6$ days. Construct a $98\%$ confidence interval for the true proportion of time this student is late. 

A previous study found that your school consists of $60\%$ White/Caucasian students. You want the $98\%$ confidence interval for the proportion of White/Caucasian students to be no more than $.05$ away from the true proportion. How many students must you include in a sample to create this confidence interval? 

You wish to estimate with $90\%$ confidence the population proportion of people in Gen-Z that use social media. If you want your estimate to be accurate within $4\%$ of the population proportion, what is the minimum sample size needed?