anonymous
  • anonymous
Please help........ The 75th percentile on a test corresponded to a score of 700, while the 25th percentile corresponded to a score of 450. Which is greater, or equal or no solution. A. 800 B. A 95th percentile score
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
A i think
anonymous
  • anonymous
.... i dont need the answer i need an explanation
anonymous
  • anonymous
Hi. Are you still here? :)

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anonymous
  • anonymous
yes
phi
  • phi
I think we must assume it is a normal distribution Based on the info 50% of the area under the curve (i.e. from 25% to 75%) is between 450 and 700
anonymous
  • anonymous
yea its a normal distribution
phi
  • phi
the mean will be exactly in the middle of 450 and 700 that will be the average of those two numbers 1150/2 = 575 using a z-table, we find that 50% of the area is between -0.674 and + 0.674 std deviations the difference from the mean 575 to 700 is 125 so the 175 corresponds to 0.674 std deviations we can find the std deviation using a proportion \[ \frac{125 }{0.674}= \frac{x}{1} \] x= 185 (roughly)
anonymous
  • anonymous
hmmmmmm
anonymous
  • anonymous
well the answer is no solution i want to understand why that is.
phi
  • phi
If we know it is a normal distribution it seems we can answer the question
anonymous
  • anonymous
oh ... im so confused hang on let me type what it says
anonymous
  • anonymous
Scoring Scales on a test are not necessarily linear, so while it may look like you can line up the difference in percentiles with the difference in score, you cannot make any predictions about other percentiles. For all you know 750 could be the 95th percentile score- or 963 could be. All you know is that 25% of the scores are <= 450, while 50% of the scores are > 450 and <=700, and 25% of the scores are >700.
phi
  • phi
Is that the answer?
anonymous
  • anonymous
yea.. but i don't understand...
phi
  • phi
is there any more to the question?
anonymous
  • anonymous
no that's all...
phi
  • phi
ok the only way to answer the question is you need to know what percent go with what score (in particular for what percent are below the score 800) and we then compare that to 95% If they do not tell us this info, then we can't answer the question. However, if they told us the test results were "normally distributed" that is a clue that let's us figure out the answer. (because all normal distributions have the same statistics, and we have z-tables) if we are not told the test is normally distributed, then we don't have enough info.
anonymous
  • anonymous
ohhh hmmm okay so basically they have to mention that it's a normal distribution?
phi
  • phi
or they have to tell us the distribution (there are other kinds ) or they have to give a table. when you posted the question, notice the first thing I asked was: I think we must assume it is a normal distribution (I was guessing you left that out of the question), because I know you can't answer the question unless we know more than what was given.
anonymous
  • anonymous
ohhh oops sorry
phi
  • phi
Not a criticism, just explaining the way I think.
anonymous
  • anonymous
got it yea i think i understand now thanks phi!!!

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