Statistical proble: Andre is fearless circus performer who gets shot from a special cannon during the grand finale of the show and is supposed to land on a safety net at the other side of the arena. The distance he travels varies, but is normally distributed with a mean of 150 feet and a standard deviation of 10 feet. The landing net is 30 feet long. Q: To maximize the probability of landing on the net, how far away from the cannon should he position the nearest edge of the net?
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!
Statistical proble: Andre is fearless circus performer who gets shot from a special cannon during the grand finale of the show and is supposed to land on a safety net at the other side of the arena. The distance he travels varies, but is
Q: To maximize the probability of landing on the net, how far away from the cannon should he position the nearest edge of the net?
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