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The table shows the scores for eight students on a 100-point test.
Katie Roxy Mika Skylor Shae Peyton Anijah Kahlan
89 79 94 86 81 77 78 88
Find the percentile ranks for the scores of Katie and Anijah.


Lily and Johnae took two different science tests. The scores on both were normally distributed.
Score on Test Mean of Scores Standard Deviation of Scores
Lily 78 71 4.3
Johnae 75 62 5.5
Use z-scores to determine which student scored better, relative to the other scores in each class. Show all your work.

*** I just don't get how to do these. Thanks for any help!!

Respuesta :

For the first one, a percentile rank is the percentage of students who scored below someone.  With 8 students, Katie's score is the second-highest, so six students scored below her, so her rank is 6/8*100=75%.  Anijah's is the second-lowest, so her rank is 1/8*100=12.5%.

For the second, the z-score is the amount of standard deviations above the mean a given value is.  Lily's is (78-7.1)/4.3=1.63, and Johnae's is 2.36.  Thus, Johnae scored better relative to other students, despite receiving a lower numerical score.

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