Il, trust me, I get your point. Yes, the 85th vehicle was in the 45-49 mph speed interval. But the question is not asking "what was the speed of the 85th vehicle?". The question is "what is the 85th percentile speed?". This needs to be calculated.
OK, so here's a fundamental difference we have. The more I think of it, the better and better this problem is looking as a great problem for the PE exam. Equations should never be blindly followed and especially not when you know they violate the underlying principles. Much earlier in this thread I wrote about the "plug and chug" mentality. (1)
Again, if there were 100 recorded individual speeds, the speed of the 85th fastest car would be the answer (of course, we have no idea what this is in this problem).
And another big disagreement here: of course we have an idea what speed each and every car is travelling because we assume they are normally distributed. 100 samples are surely in the realm of the large numbers. (2)
And let me ask you to do this final thing... putting away all previous discussion in this thread: Go back to the fundamentals of 85th percentile speeds (I gave this http://onlinemanuals...ntile_speed.htm but there are surely other sources). And ask yourself this: can binning speeds change the underlying principles of 85th percentile speeds? That is, can the throwing away of information (exact MPH speed) in favor of the convenience for collecting tick marks in a bin on a form, change the underlying process that drives the use of 85th percentile speeds?
Here's what I'm understanding you to say: You agree the 85th fastest vehicle is the definition of the 85th percentile speed. You agree the 85th fastest vehicle is in the 45-49 bin. You want to use an equation that assumes all speeds in a bin are actually at the mean of the bin, even though you know this is not representative of reality. You come up with an answer that you know does not reflect reality. All in favor of following an FDOT recommended process. (3)
Still, I appreciate the discussion especially since we've kept it civil of late! I find this problem fascinating... not sure exactly why.
It appears that you are continuing to look at this problem from a mathematical point of view instead of an engineering point of view. I do very much disagree with your lack of appreciation for pre-established engineering formulas/equations. They are there for a reason! They have been established and agreed upon by engineers before us. Who are we to disregard industry standards and use our own? Why reinvent the wheel? There is an established and agreed upon procedure for determining the 85th percentile speed from collected data. Period. You don't need to agree with it or even like it. But it is the correct way of solving this problem. And it is the answer to this problem and to the original poster's question. I'm actually surprised you think this is such a good problem for the PE exam given that the correct solution is derived from the previously shown method leading to answer C. With all due respect, you'd get this problem wrong if you answered D on the exam. Do you not agree with that?(2)
You are right, we do disagree here. I think that once the exact speed is thrown out in exchange for speed interval tick marks during the data collection, we now no longer know the exact speed each of the cars within an interval was traveling.(3)
Yes, you summed up my answer correctly. I see absolutely no problem with using an industry accepted method to calculate the 85th % speed even if it does not reflect reality as you say it. The same way I'd order 18" pipe even if my calculations showed a 16.2" diameter was needed given my Q (because I know that they don't make 17" pipe). If I calculated a design speed of 54, I'd post 50, not 55. If I was designing curb and gutter on street plans for the City of Anyville, I'd sure as heck use their City Standard Plan for C&G (even though I may personally prefer Std 120-2 of the SPFPWC), if I was calculating the Q coming off of a proposed developed site, I might use a coefficient of runoff a little higher than "reality", to be conservative. Etc. etc.
I hope you get my point. Again, with all due respect, the answer to the original question is C and the previous calculations are correct. That answers the question asked by the original poster.
I'm not really interested in going back and forth any longer about how the answer "should be" this or that. The correct answer is C. If you have questions about how C is derived, I'd be happy to answer. But if you continue to simply repeat yourself that the answer "should be" D, then there isn't much more I can say. Thanks.
Edited by ptatohed, 30 April 2012 - 08:56 PM.