On a particular stretch of highway, the speed limit is 65 mph. Speeds of cars on that stretch have a mean of 71 mph with a standard deviation of 5 mph. a. Would it be unusual to observe a car driving 60 mph or less on this stretch of highway? Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution. b. If we observe 100 cars along this highway, how many of them do we expect to be obeying the speed limit? Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution. c. A highway patrol officer pulls a car over for driving 75 mph. The driver argues that he was “going with the flow of traffic” and that the officer is unfairly singling him out for speeding. Does the driver have a point? Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution. Finally, recall the highway problem: the mean speed on a stretch of highway is 71mph with a standard deviation of 5mph. We all know that slow drivers are often just as dangerous as fast drivers. How slow are the slowest 10% of drivers traveling on this stretch of highway? Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution.
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!
On a particular stretch of highway, the speed limit is 65 mph. Speeds of cars on that stretch have a mean of 71 mph with a standard deviation of 5 mph.
a. Would it be unusual to observe a car driving 60 mph or less on this stretch of highway? Explain your answer using the appropriate statistics and a correctly labeled and shaded
b. If we observe 100 cars along this highway, how many of them do we expect to be obeying the speed limit? Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution.
c. A highway patrol officer pulls a car over for driving 75 mph. The driver argues that he was “going with the flow of traffic” and that the officer is unfairly singling him out for speeding. Does the driver have a point? Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution.
Finally, recall the highway problem: the mean speed on a stretch of highway is 71mph with a standard deviation of 5mph. We all know that slow drivers are often just as dangerous as fast drivers. How slow are the slowest 10% of drivers traveling on this stretch of highway?
Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution.
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