Question 181991: Hi Tutors! This is one of the questions I'm stuck on. Please show me how to do it.
A traffic officer has a concealed radar unit that she uses to measure the speed of traffic crossing a bridge. She finds that the mean speed is 84km/h and the standard deviation is 5km/h.
a) What probability distribution is most likely to model the speed of the traffic crossing the bridge? Give reasons for your choice that are related to the problem and give any parameters for the distribution.
b) If the speed limit on the bridge is 90km/h, find out how many out of 200 cars she would expect to find to be breaking the limit.
Thank you very very much for your help tutors!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A traffic officer has a concealed radar unit that she uses to measure the speed of traffic crossing a bridge. She finds that the mean speed is 84km/h and the standard deviation is 5km/h.
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a) What probability distribution is most likely to model the speed of the traffic crossing the bridge? Give reasons for your choice that are related to the problem and give any parameters for the distribution.
Ans: Normal Distribution because the data is continuous, numerical, and tends
to cluster around an average speed.
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b) If the speed limit on the bridge is 90km/h, find out how many out of 200 cars she would expect to find to be breaking the limit.
If the mean is at 84 km/h, 90km/h is (90-84)/5 = 6/5 = 1.2 standard deviations
above the mean.
The percent of the population that is more than 1.2 standard deviations above the mean is 11.5%.
11.5% of 200 is 23 persons.
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Cheers,
Stan H.
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