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 41 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) If the true mean is .9220 with a standard deviation of 0.0060, within what interval will 90 percent of the sample means fall? (Round your answers to 4 decimal places.) The interval is from _______ to _________ (b) If the true mean is .9220 with a standard deviation of 0.0060, what is the sampling distribution of X⎯⎯⎯X¯ ? Exactly normal with μ = .9220 and σ = 0.0060. Approximately normal with μ = .9220 and σ = 0.0060. Exactly normal with μ = .9220 and σx⎯⎯=0.0060/41‾‾‾√.σx¯= 0.0060/41. Approximately normal with μ = .9220 and σx⎯⎯=0.0060/41‾‾‾√.σx¯= 0.0060/41. 1 2 3 4 (c) What theorem did you use to answer part (b)? Central Limit Theorem Chebyshev's Theorem Pythagorean Theorem Law of Large Numbers
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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 41 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.
(a) If the true mean is .9220 with a standard deviation of 0.0060, within what interval will 90 percent of the sample means fall? (Round your answers to 4 decimal places.)
The interval is from _______ to _________
(b) If the true mean is .9220 with a standard deviation of 0.0060, what is the sampling distribution of X⎯⎯⎯X¯ ?
- Exactly normal with μ = .9220 and σ = 0.0060.
- Approximately normal with μ = .9220 and σ = 0.0060.
- Exactly normal with μ = .9220 and σx⎯⎯=0.0060/41‾‾‾√.σx¯= 0.0060/41.
- Approximately normal with μ = .9220 and σx⎯⎯=0.0060/41‾‾‾√.σx¯= 0.0060/41.
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(c) What theorem did you use to answer part (b)?
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Central Limit Theorem
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Chebyshev's Theorem
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Pythagorean Theorem
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Law of Large Numbers
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