In hydrology, the annual precipitation height in a basin corresponds to Normal and Log-Normal distributions with an average of 55 standard deviations of 10. Make the following calculations with both distributions to the table below. Normal Distribution Solution Log-Normal Distribution Solution a) What are the probability of annual precipitation heights between 42 and 48 cm in the future? b) What is the probability that annual precipitation heights are at least 34 cm? c) What is the probability of annual rainfall heights to exceed 70 cm?
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 hydrology, the annual precipitation height in a basin corresponds to Normal and Log-Normal distributions with an average of 55 standard deviations of 10. Make the following calculations with both distributions to the table below.
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Log-Normal Distribution Solution |
a) What are the
b) What is the probability that annual precipitation heights are at least 34 cm?
c) What is the probability of annual rainfall heights to exceed 70 cm?
Equation: ? = ??? –(1/2) ?^2
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