In a Gallup poll of $450$ employed adults, $82\%$ said they prefer working remotely at least part of the time. Among the $450$ respondents, how many said they prefer working remotely?

A news website asks visitors to vote online on whether a newly released public service advertisement is “respectful” or “disrespectful.” Of the $1500$ visitors who responded, $1230$ said the ad was respectful and $270$ said it was disrespectful. Construct a $95\%$ confidence interval estimate of the true proportion of all viewers who believe the ad is respectful.

A technician is testing the consistency of a machine that cuts sheets of cardboard. The sample variance of the thickness of $20$ cardboard sheets is found to be $25{\text{ mm}}^2$. Assume the thickness values are normally distributed. Construct a $90\%$ confidence interval for both the population variance and the population standard deviation.