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ptc24 at 10:43pm on 04/05/2010
ptc24 at 10:43pm on 04/05/2010So I found a source of information about human height. My source says:
I won't show you those means and standard deviations.
The question - select a random man and a random woman from the population described above. What is the probability that the man will be taller than the woman. Assume normal distributions, that no two people have precisely the same height, etc. In python terms, what's the probability that random.normalvariate(male_mean, male_stdev) > random.normalvariate(female_mean, female_stdev) will return True?
I monte carloed the results, so I have a good idea what the answer should be. Surprisingly it comes out quite close to one of the nice round numbers listed below. I'm not looking for calculations or mathematical reasoning here, just your gut instinct.
The most recent National Health and Nutrition Examination Survey (NHANES III), conducted in 1988–1994 by the United States National Center for Health Statistics, reports the cumulative distribution of height in inches for males and for females in the 20–29 age bracket (U. S. Census Bureau 1999). The data for each sex have the means and standard deviations in
Table 1 and each follow a normal distribution reasonably well.
I won't show you those means and standard deviations.
The question - select a random man and a random woman from the population described above. What is the probability that the man will be taller than the woman. Assume normal distributions, that no two people have precisely the same height, etc. In python terms, what's the probability that random.normalvariate(male_mean, male_stdev) > random.normalvariate(female_mean, female_stdev) will return True?
I monte carloed the results, so I have a good idea what the answer should be. Surprisingly it comes out quite close to one of the nice round numbers listed below. I'm not looking for calculations or mathematical reasoning here, just your gut instinct.
Poll #3006 More height dimorphism
This poll is closed.
Open to: Registered Users, detailed results viewable to: All, participants: 12
Open to: Registered Users, detailed results viewable to: All, participants: 12
Based on the assumptions above, what is the probability that a randomly selected man will be taller than a randomly selected woman?
View Answers
0.6
1 (8.3%)
0.7
2 (16.7%)
0.8
2 (16.7%)
0.85
3 (25.0%)
0.9
2 (16.7%)
0.925
0 (0.0%)
0.95
2 (16.7%)
0.975
0 (0.0%)
0.99
0 (0.0%)
0.995
0 (0.0%)
0.999
0 (0.0%)
>0.9995
0 (0.0%)
(no subject)
(no subject)
I visualised some normal distribution humps in my head and then used gut instinct about what I thought they'd end up looking like. I'm not sure if that counts as disallowed mathematical reasoning :-)
I hope you will be posting the real answer at some stage? (Does DW have the ability to close a poll to further input while continuing to show the answers?)
(no subject)
Comments such as yours and naath's are welcome and very interesting.