SOLUTION: What are the probabilities that a student will receive an A, B, C, D, and F in a class? (using standard grading scale: A=90-100, B=80-89, C=70-79, D=60-69, F=0-59)? Thank you!!

Algebra ->  Probability-and-statistics -> SOLUTION: What are the probabilities that a student will receive an A, B, C, D, and F in a class? (using standard grading scale: A=90-100, B=80-89, C=70-79, D=60-69, F=0-59)? Thank you!!      Log On


   

Question 265376: What are the probabilities that a student will receive an A, B, C, D, and F in a class? (using standard grading scale: A=90-100, B=80-89, C=70-79, D=60-69, F=0-59)?
Thank you!!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
What are the probabilities that a student will receive an A, B, C, D, and F in a class? (using standard grading scale: A=90-100, B=80-89, C=70-79, D=60-69, F=0-59)?
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If you assume a normal distribution proceed as follows:
The range from 0 to 100 is 6 sigma
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If 6*sigma = 100
sigma = 100/6 = 16.67
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If you put the mean of the distribution at 70,
z(79) = (79-70)/16.67 = 0.5399
z(70) = (70-70)/16.67 = 0
P(70< x < 79) = P(0< z < 0.5399) = 0.2054 = 20.54% (percent that get "C"
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Similarly: P(80< x < 89) = 14.71% (percent that get "B"
P(90 < x < 100) = 7.92% (percent that get "A"
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I'll leave F and D to you.
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Cheers,
Stan H.