In western Kansas, the summer density of hailstorms is estimated at about 2.0 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square mile. A crop insurance company has insured a tract of 7 square miles of Kansas wheat land against hail damage. Let r be a random variable that represents the number of hailstorms this summer in the 7-square-mile tract.(a) What is λ for the 7-square-mile tract of land? Round λ to the nearest tenth (b) If there already have been two hailstorms this summer, what is the probability that there will be a total of four or more hailstorms in this tract of land? Compute P(r≥ 4 | r ≥ 2). (Use 4 decimal places.)(c) If there already have been three hailstorms this summer, what is the probability that there will be a total of fewer than six hailstorms? Compute P(r < 6 | r ≥ 3). (Use 4 decimal places.)
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!
In western Kansas, the summer density of hailstorms is estimated at about 2.0 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square mile. A crop insurance company has insured a tract of 7 square miles of Kansas wheat land against hail damage. Let r be a random variable that represents the number of hailstorms this summer in the 7-square-mile tract.(a) What is λ for the 7-square-mile tract of land? Round λ to the nearest tenth (b) If there already have been two hailstorms this summer, what is the
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