Vehicle speed on a particular bridge in China can be modeled as normally distributed If 5% of all vehicles travel less than 39.12 m/h and 10% travel more than 73.24 m/h, what are the mean and standard deviation of vehicle speed? [Note: The resulting values should agree with those given in the cited article.] What is the probability that a randomly selected vehicle’s speed is between 50 and 65 m/h? What is the probability that a randomly selected vehicle’s speed exceeds the speed limit of 70 m/h?
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!
Vehicle speed on a particular bridge in China can be modeled as
- If 5% of all vehicles travel less than 39.12 m/h and 10% travel more than 73.24 m/h, what are the mean and standard deviation of vehicle speed? [Note: The resulting values should agree with those given in the cited article.]
- What is the probability that a randomly selected vehicle’s speed is between 50 and 65 m/h?
- What is the probability that a randomly selected vehicle’s speed exceeds the speed limit of 70 m/h?
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