SOLUTION: Please help me solve part (c), what does it mean. In the states, the speed of motorists travelling on the states highway is uniformly distributed between 55 and 115 miles per hour

Question 1077635: Please help me solve part (c), what does it mean.
In the states, the speed of motorists travelling on the states highway is uniformly distributed between 55 and 115 miles per hour.
(a) Derive the density function for speed of motorists. Draw a graph to explain your answer.
(b) If the speed of a motorist was checked at random, what is the probability that it will be travelling between 65 and 85 miles per hour?
(c) A study by highway safety professionals find that motorists travelling at speeds above the third quartile (75th percentile) are highly prone to accidents. They ask the Governor of the states to ban travelling at speeds above the third quartile. What should be the speed limit set by the Governor?

Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
The quartiles can be found from the range of speeds: 115-55 = 60 and 60/4 = 15, so the quartiles are:
55-70 1st quartile
70-85 2nd quartile
85-100 3rd quartile
100-115 4th quartile <<< Part (c) indicates driving in this quartile ("above the 3rd quartile") is most dangerous
Speed limit should be set at 100.
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Note that the median is used to find the middle of the data (and then quartiles are determined based on an ordered set of the data, 1/4 on bottom, 2nd 1/4 next group, 3rd 1/4/ next group, 4th 1/4 highest group), in this case I used the mean, but the problem states the speeds driven are uniformly distributed so this works.
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