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.

Question

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:
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 1

Look at the normal distribution table.

 

an A is 1.5 standard deviations above the mean, which is approximately 6.7%......so 7%

A B is between .5 and 1.5 standard deviations above the mean, so according to the table, 24.2%...rounding off to 24%.

A C is .5 below to .5 above, which is 38.2%, rounded to 38%

A D is between 1.5 and .5 below the average, which will be the same percentage as a B, so 24%

An F is below 1.5 standard deviations below the average, which will be the same as an A, So 7%

 

This all just came from the graph and percentages from a normal curve and normal table.

 

Hope this helped.