Question 1021333: When asked if grades are “curved” Professor Makanyanga replies that she uses the
normal curve as a guide in assigning letter grades to large classes. She first finds the average numerical grade and the standard deviation of the numerical grades, and then assigns the letter grades as follows:
Numerical grades (X) interval grade
X ≥ μ + 1.5σ A
μ + 0.5σ ≤ X < μ + 1.5σ B
μ - 0.5σ ≤ X <μ + 0.5σ C
μ - 1.5σ ≤ X < μ - 0.5σ D
X < μ -1.5σ F
In a class of 800, approximately how many students will receive each letter grade? Give
your answer to the nearest whole number.
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! The partitioning above is the same as
A: Z ≥ 1.5 (6.68%)
B: 0.5 ≤ Z < 1.5 (24.17%)
C: - 0.5 ≤ Z < 0.5 (38.3%)
D: - 1.5 ≤ X < - 0.5 (24.17%)
F: Z < -1.5 (6.68%)
along with the corresponding areas under the standard normal curve.
This means
800*0.0668 = 53.44, or 53 will get A
800*0.2417 = 193.36, or 193 will get B
800*0.383 = 306.4, or 306 will get C
800*0.2417 = 193.36, or 193 will get D
800*0.0668 = 53.44, or 53 will get F
(Notice that the total will only be 798, due to the rounding that was done.)
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