Listed below are recorded speeds (in miles/hour: mph) of randomly selected cars traveling on a section of Highwa 405 in Los Angeles (based upon data from Sigalert). That section has a posted speed limit of 65mph. Traffic engineers often establish speed limits by using the "85th percentile rule," whereby the speed limit is set so that 85% of drivers are at or below the speed limit. • Frequency Table: class width 3; midpoint of first class 56 68 68 72 73 65 75 73 72 68 65 65 73 66 71 68 74 66 71 65 73 59 75 72 66 58 70 56 75 68 75 62 60 73 61 75 74 60 73 58 75
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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