SOLUTION: The problem is: A student scored 80 for an English exam and 72 for a History exam. If the class scores were normally distributed with a mean and standard deviation for English of 7

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Question 281549: The problem is: A student scored 80 for an English exam and 72 for a History exam. If the class scores were normally distributed with a mean and standard deviation for English of 75 and 8 respectively, and for History 60 and 15 respectively, in which subject did the student achieve a higher standard, and what percentage of others achieved higher marks in each subject?
Answer by Mathematicians(84) About Me  (Show Source):
You can put this solution on YOUR website!
You want to find the Z score for each subject. You can recall, the higher z is, the smaller the graph goes which symbolize a higher tier in ranking. For a higher ranking, you want to take the greatest positive z
So, to calculate z score, you would calculate z+=+%28x+-+M%29%2Fs where x is the data, M is the mean, and s is standard deviation.
For English:
%2880+-+75%29%2F8+=+5%2F8
For History:
%2872+-+60%29+%2F+15+=+12%2F15+=+4%2F5
+4%2F5+%3E+5%2F8 => History achieved higher standard.
Now we need to find what percentage of others achieved higher marks in each subject. Unfortunately Z tables calculate Z values different and for that I cannot tell you how to use a Z table.
We calculated Z = 5/8 for English
We want to find P(z > 5/8)
You may need to do .5 - P(z = 5/8) or 1 - P(z = 5/8) depending on your Z table
Same thing with history except:
You may need to do .5 - P(z = 4/5) or 1 - P(z = 4/5) depending on your Z table.
Good luck!