Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 47 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) If the true mean is .9560 with a standard deviation of 0.0080, within what interval will 99 percent of the sample means fall? (Round your answers to 4 decimal places.) The interval is from to (b) If the true mean is .9560 with a standard deviation of 0.0080, what is the sampling distribution of X¯¯¯ ? Exactly normal with μ = .9560 and σ = 0.0080. Approximately normal with μ = .9560 and σ = 0.0080. Exactly normal with μ = .9560 and σx¯= 0.0080/47−−√. Approximately normal with μ = .9560 and σx¯= 0.0080/47−−√. 1 2 3 4 (c) What theorem did you use to answer part (b)? 1. Central Limit Theorem 2. Chebyshev's Theorem 3. Pythagorean Theorem 4. Law of Large Numbers