6.) Suppose in order to sue Diesel Dave, Environmentalist Ed needs the daily average level of sulfur dioxide emissions to exceed 3000 ppm. However, he can choose to take his mean measurement over 2, 3, or 15 days. Which number of days would maximize Environmentalist Ed's chances of suing Diesel Dave? (Hint: What does the OLT say about the variance of the sampling distribution as n changes?) 7.) Miller Beer needs its beer to be somewhat bitter, but not too bitter, in order to maximize sales revenue from Wisconsin Bros. The standard way of measuring bitterness is the number of IBUs or International Bitterness Units. A batch of Old Milwaukee beer has on average 24 IBUs with a standard deviation of 3.1 IBUs, moreover IBUs are distributed normally across beer batches. If the batch of beer has more than 28 IBUs Wisconsin Bros declare the beer "liberal, coastal elite beer" and refuse to drink it. If the beer has fewer than 18 IBUs Wisconsin Bros declare the beer "weak" and also refuse to drink it. What is the probability that a randomly drawn batch of beer will be undrinkable to Wisconsin Bros? 8.) Suppose that Miller Beer samples people's perceptions of the quality of Old Milwaukee beer. Respondents are asked to evaluate the beer on a scale of 1 to 10. The modal response is a 9 amongst sampled Wisconsin Bros, while the mean is 7.7 with a standard deviation of 2. Suppose you conduct 27 samplings to generate your point estimate of 7.7 as the mean evaluation of Old Milwaukee beer. If you want to use the central limit theorem to evaluate the likelihood that the next sampling will generate a mean evaluation greater than 8.0 which of the three assumptions is clearly violated and why (Hint: If you don't think it's the independent or identical assumption, then it must be the normality assumption)? 9.) Look back at the information in the previous question, but assume that you will use 35 samplings to avoid violating the needed assumption to use the central limit theorem. What is the probability of getting a mean evaluation greater than 8