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Answer:
The z-score for the statistics test grade is of 1.11.
The z-score for the calculus test grade is 7.3.
Due to the higher z-score, the student performed better on the calculus test relative to the other students in each class
Step-by-step explanation:
Z-score:
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In this question:
The grade with the higher z-score is better relative to the other students in each class.
Statistics:
Mean of 79 and standard deviation of 4.5, so
Student got 84, so
The z-score is:
The z-score for the statistics test grade is of 1.11.
Calculus:
Mean of 69, standard deviation of 3.7, so
Student got 96, so
The z-score is:
The z-score for the calculus test grade is 7.3.
On which test did the student perform better relative to the other students in each class?
Due to the higher z-score, the student performed better on the calculus test relative to the other students in each class
when
is in quadrant II, so