Several years ago, ballots in Champaign-Urbana contained the following question to assess public opinion on an issue: "Should the State of Illinois legalize and regulate the sale and use of marijuana in a similar fashion as the State of Colorado?" Suppose that we would like to understand Champaign-Urbana's 2017 opinion on marijuana legalization. To satisfy our curiosity, we obtain a random sample of 120 Champaign-Urbana residents and find that 87 support marijuana legalization. (a) Construct and interpret a 99% confidence interval for p. (b) Calculate and interpret the 95% confidence lower bound. (c) Suppose that a pollster wants to estimate the true proportion of Champaign-Urbana residents that support marijuana legalization to within 0.04, with 95% confidence. How many Champaign-Urbana residents should this pollster survey? Assume the pollster has no prior knowledge about the true proportion. (d) Now assume the pollster believes that support for legalization is somewhere between 65% and 85% and they would like to estimate the true proportion of Champaign- Urbana residents that support marijuana legalization to within 0.04, with 90% confidence. How many Champaign-Urbana residents should this pollster survey? Hint: Even though the assumed possible value for p falls within a range this time, you'll want to choose the "safest" one. See part b for inspiration