Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 83 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 83 tons and standard deviation σ = 1.2 ton. (a) What is the probability that one car chosen at random will have less than 82.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 19 cars chosen at random will have a mean load weight x of less than 82.5 tons of coal? (Round your answer to four decimal places.)Suppose the weight of coal in 19 cars selected at random had an average x of less than 82.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? a) Yes, the probability that this deviation is random is very small. b) Yes, the probability that this deviation is random is very large. c) No, the probability that this deviation is random is very small. d) No, the probability that this deviation is random is very large.
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!
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 83 tons of coal into each car. The actual weights of coal loaded into each car are
(b) What is the probability that 19 cars chosen at random will have a mean load weight x of less than 82.5 tons of coal? (Round your answer to four decimal places.)
Suppose the weight of coal in 19 cars selected at random had an average x of less than 82.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why?
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