(2) In a certain achievement test, the seventh grade mean is 28.00 and SD is 4.80; and the eighth grade mean is 31.60 and SD is 4.00. What percent of the seventh grade is above the mean of the eighth grade? What percent of the eighth grade is below the mean of the seventh grade ?
Answers
Given : In a certain achievement test,
the seventh grade mean is 28.00 and SD is 4.80;
the eighth grade mean is 31.60 and SD is 4.00.
To Find :
What percent of the seventh grade is above the mean of the eighth grade? What percent of the eighth grade is below the mean of the seventh grade ?
Solution:
Z score = ( Value - Mean ) /SD
percent of the seventh grade is above the mean of the eighth grade
eighth grade mean is 31.60 = > Value = 31.6
the seventh grade mean is 28.00 and SD is 4.80;
=> Mean = 28 and SD = 4.8
Z score = ( 31.6 - 28)/4.8 = 0.75
=>Z score 0.75 => 77.34 %
percent of the seventh grade is above the mean of the eighth grade = 100 - 77.34 % = 22.66 %
percent of the eighth grade is below the mean of the seventh grade
seventh grade mean is 28.00 => Value = 28
eighth grade mean is 31.60 and SD is 4.00.
=> Mean = 31.6 and SD = 4.00.
Z score = (28 - 31.6)/4 = -0.9
=>Z score 0.75 => 18.41 %
percent of the eighth grade is below the mean of the seventh grade =18.41 %
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