Question 977304: Question 1: A test has a mean of 30 and a standard deviation of five.
Jackie has scored in the 57th percentile.
Ethan has a T score of 70.
Lan has obtained a z score of –0.2.
Salvatore has received a raw score of 27.
On the basis of the information provided, answer the following questions:
Who has scored the highest?
Who has scored the lowest?
*I am completely lost on this question. Can anyone explain how to do it so I can complete the rest of the problems I have that are similar* Thank You!
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Question 1: A test has a mean of 30 and a standard deviation of five.
Comment:: Convert all the scores to z-scores.
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Jackie has scored in the 57th percentile.
z-score = invNorm(0.57) = 0.176
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Ethan has a T score of 70.
Comment:: Are you sure? That would be 70 standard deviations above the mean.
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Lan has obtained a z score of –0.2.
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Salvatore has received a raw score of 27.
z(27) = (27-30)/5 = -3/5 = -0.6
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On the basis of the information provided, answer the following questions:
Who has scored the highest?
Excluding that "T"score, Jackie's score is highest.
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Who has scored the lowest?
Salvatore's is the lowest.
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Cheers,
Stan H.
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Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Throw out the Z-score and the raw score since both of those are below the mean, whereas the 57th percentile is at least a little bit above the mean. But your T-statistic of 70 doesn't mean much without some knowledge of the size of the sample from which the statistic was derived.
Be that as it may, I was able to bound the problem thus: The minimum sample size must be 4 because you gave four, albeit differently stated, test results. The maximum sample size I calculated to be 25, because if the sample size is larger than 25 the raw score is larger than 100 which I assume to be the upper limit on the raw score.
Either way, the minimum raw score for a t-statistic of 70 is 58 which is way larger than the 57th percentile.
Having said all that, this question is magnificently stupid and made so by the inclusion of a t-statistic and z-score comparison. Z-scores are for when you know  and the t-distribution is for when you don't know . Since the use of these two sample statistics is mutually exclusive, why would anyone ask you to do something so dumb as to compare the relative magnitude of the two for a given set of data?
John
My calculator said it, I believe it, that settles it
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