The average number of acres burned by forest and range fires in a large county is 4,300 acres per year, with a standard deviation of 700 acres. The distribution of the number of acres burned is norma a. Compute the probability that more than 5,000 acres will be burned in any year. b. Determine the probability that fewer than 4,000 acres will be burned in any year. c. What is the probability that between 3,500 and 4,100 acres will be burned? d. In those years when more than 5,500 acres are burned, help is needed from eastern-region fire teams. Determine the probability help will be needed in any year. a. The probability that more than 5,000 acres will be burned is (Round to four decimal places as needed.) b. The probability that fewer than 4,000 acres will be burned is (Round to four decimal places as needed.) c. The probability that between 3,500 and 4,100 acres will be burned is (Round to four decimal places as needed.) d. The probability help will be needed is (Round to four decimal places as needed.)
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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