At noon there were 500 litres of clean water in an outside swimming pool. At 1 pm it starts to rain, and the acid rain is pouring into the pool at the rate of 5 litres per hour. The concentration of the acid is the rain is constant but unknown. The water in the pool is mixed well and drained at the rate of 5 litres per hour. After 100 minutes there are 16 grams of acid in the pool. What is the concentration of the acid in the rain?
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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