Bicycles arrive at a bike shop as parts in a box. Before they can be sold, they must be unpacked and assembled. Based on past experience, the bike shop owner knows that assembly times follow (roughly) a Normal distribution with a mean of 25 minutes and a standard deviation of 3 minutes. A customer walks into the bike shop and wishes to buy a bike like the one in the window, but in a different color. The shop has one, but it is still in the box, so it will need to be assembled. What is the probability that the bike will be ready within a half hour?
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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