Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of operation, and low cost. The article ''Procedure to Verify the .faximum Speed of Automatic Transmission Mopeds in Periodic Motor Vehicle Inspections"(J .of Automobile Engr.,2008: 1615-1623) described a rolling bench test for determining maximum vehicle speed. A normal distribution with mean value 46.8km/h and standard deviation 1.75 km/h is postulated. Consider randomly selecting a single such moped. a. What is the probability that maximum speed is at most 50 km/h? b.What is the probability that maximum speed is at least 48 km/h? c. What is the probability that max. imum speed differs from the mean value by at most 1.5 standard deviations?
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!
Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of operation, and low cost. The article ''Procedure to Verify the .faximum Speed of Automatic Transmission Mopeds in Periodic Motor Vehicle Inspections"(J .of Automobile Engr.,2008: 1615-1623) described a rolling bench test for determining maximum vehicle speed. A
a. What is the
b.What is the probability that maximum speed is at least 48 km/h?
c. What is the probability that max. imum speed differs from the mean value by at most 1.5 standard deviations?
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