Question 522679: The problem is this: A student has taken 5 tests, but lost her list of individual scores. She had added up 3 sets of total scores for 3 randomly pulled individual scores each time, and could remember those numbers. The 1st 3 randomly pulled scores equaled 190. The 2nd set of 3 randomly pulled scores equaled 230, and the 3rd set of 3 randomly pulled scores (all out of the same 5 scores) equaled 260. What were her individual scores on each of the 5 exams?
This is a probability problem where the means have been given,but not the standard deviation, and it's outside of the scope of our classroom lectures and our book. Can you please help me solve this?
Answer by Edwin McCravy(20067)   (Show Source):
You can put this solution on YOUR website!
Sorry, there is no one answer because
there are many, many, possibilities.
1. For example, if her scores were
30 60 70 100 100 then her random selections of three could
result in:
30+60+100 = 190, 30+100+100=230, 60+100+100=260.
2. Or, her scores could have been
50 70 70 90 100
and her sums could be 50+70+70=190, 70+70+90=230, 70+90+100=260
3. Or her scores could have been
20 60 80 90 90
and her sums could be 20+80+90=190, 60+80+90=230, 80+90+90=260
4. And it's not even necessary that any two scores be the same, or that
any score not be chosen, for this is a possibility too:
30 60 70 90 100
and her sums could be 30+70+90=190, 60+70+100=230, 70+90+100=260
None of those scores are the same and all five were included in at least
one of the random selections.
We could go on and on and on. There is just not enough information to
determine her individual scores on each of the 5 exams, as the above
examples show.
Edwin
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