Suppose in two local counties, the locals have toad collecting contests. In the two largest,the average number of toads collected by contestants is µ1 = 43 with σ1 = 11 and µ2 = 55(Obviously a county with a larger toad population) with σ2 = 15. Cindy entered into contestnumber one and collected 56 toads and her sister Mindy entered into contest number two andcollected 73 toads. Which sister did better in the contest?
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!
Suppose in two local counties, the locals have toad collecting contests. In the two largest,
the average number of toads collected by contestants is µ1 = 43 with σ1 = 11 and µ2 = 55
(Obviously a county with a larger toad population) with σ2 = 15. Cindy entered into contest
number one and collected 56 toads and her sister Mindy entered into contest number two and
collected 73 toads. Which sister did better in the contest?
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