8.) On a particular stretch of highway, the speed limit is 65 mph. Speeds of car

Question

8.) 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

Explanation / Answer

a) p [x < 60] = p [Z < (60 - 71) / 5] = p [Z < -2.2] = 0.0139

Yes it is unusual, since p = 0.0139 < 0.05

b) required number of cars = 100 * p [x > 65 - 71)/5] = 100*p [Z > -1.2] = 100*0.8849 = 88.49

The required number of cars are 89

c) p [x > 75] = p [Z > 75 - 71) / 5] = p [Z > 0.8] = 0.2119

The driver does not have a point, since p = 0.2119 > 0.05

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