A reputable weather service issues precipitation forecasts that indicate the likelihood of measurable precipitation at a specific point during a given time period. Suppose that if a measurable amount of rain falls during the next 24 hours, a river will reach flood stage and a business will incur damages of $150,000. The weather service has indicated that there is a 35% chance of a measurable amount of rain during the next 24 hours. Complete parts a and b below. a. Construct the probability distribution that describes the potential flood damages. Sample Point Measurable amount of rain Not a measureable amount of rain Loss, x $ p(x) (Type integers or decimals. Do not round.) b. Find the firm's expected loss due to flood damage. The expected loss is $. (Type an integer or a decimal. Do not round.)
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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