For all problems, round every calculation to three decimal places.

1. Jeremy recently created a survey that asked randomly selected U.S. adults how often they played video games (often, sometimes, or never). Of the 3,930 respondents, 1,688 said they play video games. Of those who played, 844 said that they played often. Find a 99% confidence interval for the proportion of U.S. adults who play video games often. Show all work.
2. Prof. Smith was in St. Joseph, Missouri to witness totality for the solar eclipse that crossed the U.S. in 2017 (true story!) and noticed that the temperature dropped noticeably during totality (when the sun is completely covered by the moon). 90 amateur scientists across the country recorded an average temperature change of -10.4 F with a standard deviation of 6 F.
   1. Find a 90% confidence interval for the mean temperature drop in degrees Fahrenheit ( F) during totality.
   2. If we want a margin of error of only 0.1 F, what sample size is needed?