The United States exports hundreds of thousands of metric tons of wood chips each year to Japan. The amount exported varies from year to year with an approximately Normal distribution with a mean of 282 thousand (282,000) metric tons and a standard deviation of 58 thousand metric tons. (a) What is the probability of U.S wood chip exports to Japan exceeding 410 thousand metric tons in a given year? (b) What is the probability of U.S. wood chip exports being between 260 and 340 thousand metric tons in a given year? (c) How many tons of wood chips would need to be exported in a year in order for that year to rank in the top 15% of years?
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!
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