SOLUTION: Suppose you earned 100 points on an exam. Under which of the following conditions did you earn the best grade? When: a. μ = 80 and σ = 10 b. μ = 80 and σ = 5

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Question 527163: Suppose you earned 100 points on an exam. Under which of the following conditions did you earn the best grade?
When:
a. μ = 80 and σ = 10
b. μ = 80 and σ = 5
c. μ = 105 and σ = 10
d. μ = 105 and σ = 5
Make sure to justify your response with one to two sentences.
Found 2 solutions by oberobic, Edwin McCravy:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
With μ = 80 and σ = 5, a score of 100 is +4σ, which is > 99.99 percentile.

Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
Calculate all the z-scores using the formula z = %28x-mu%29%2Fsigma
where x = 100.  z-score is a measure of how far above the average
a score is if the z-score is positive, or how far below average a
score is if the z-score is negative.

a. μ = 80 and σ = 10

z = %28x-mu%29%2Fsigma = %28100-80%29%2F10 = 20%2F10 = 2 

b. μ = 80 and σ = 5

z = %28x-mu%29%2Fsigma = %28100-80%29%2F5 = 20%2F5 = 4

c. μ = 105 and σ = 10

z = %28x-mu%29%2Fsigma = %28100-105%29%2F10 = -5%2F10 = -0.5

d. μ = 105 and σ = 5

z = %28x-mu%29%2Fsigma = %28100-105%29%2F5 = -5%2F5 = -1

Answer:  b. 

The score of 100 is below average in "c" and "d".  It's above average in
"a" and "b".  "b" is farther above the average than "a" is. 

Edwin