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Q: seven obversation are drawn from a population with an unknown continuous distribution. What is the probability that the least and greates
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Q: seven obversation are drawn from a population with an unknown continuous distribution. What is the probability that the least and greates
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Question 1164784: Please help me to solve this problem :
Q: seven obversation are drawn from a population with an unknown continuous distribution. What is the probability that the least and greatest obversation bracket the median? Found 3 solutions by greenestamps, solver91311, ikleyn:Answer by greenestamps(13215) (Show Source):
The question asks for the probability that the number in the middle is between the least number and the greatest number. That probability is obviously 1.
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After reading responses from other tutors, I see now that the problem is indeed stated poorly.
I interpreted the question as asking for the probability that the least and greatest of the seven observations bracketed the median OF THOSE SEVEN OBSERVATIONS. That was a trivial question to answer.
It is a completely different question -- perhaps impossible to answer -- if the "median" is the median of the whole population.
You are going to make seven observations of the data. There is a finite probability that all seven of the observations are greater than the median, and there is an equal probability that all seven observations are less than the median. Since the definition of the median of a set of data is that value such that exactly half of the values are greater and half of the values are less than the median, the probability that any given observation is greater than the median is 0.5, and the probability that any given observation is less than the median is also 0.5.
The situation is precisely the same as flipping a fair coin seven times in a row. And the question asked is what is the probability that you don't get either seven heads in a row or seven tails in a row.
You can do your own arithmetic.
John
My calculator said it, I believe it, that settles it
In my view, the problem is posed / formulated INCORRECTLY.
Had it be formulated correctly, it would state that the distribution is uniform on certain interval
(instead of saying "continuous")
and would ask " What is the probability that the least and the greatest
observations bracket the mid point of the interval"
(instead of using the term "median", which is AMBIGUOUS in this context).
It is Math, where every word/term in the condition does matter, and every inaccurately used term
breaks the meaning totally or makes it unclear.
How the problem is posed in the given post, it is not a Math.
