Question

***PLEASE SHOW HOW TO SOLVE IN EXCEL*** NOT HANDWRITTEN

5) The letter grades on the midterm exam given in a large managerial statistics class are normally distributed with mean 75 and standard deviation 9. The instructor of this class wants to assign an A grade to the top 10% of the scores, a B grade to the next 10% of the scores, a C grade to the next 10% of the scores, a D grade to the next 10% of the scores and an F grade to all scores below the 60th percentile of this distribution. For each possible letter grade, find the lowest acceptable score.

Answer 1

Population mean, µ = 75

Population standard deviation, σ = 9

Lowest acceptable score for Grade A:

top 10% = above 90% of the scores

Z score at p = 0.9 using excel = NORM.S.INV(0.9) = 1.2816

Value of X = µ + z*σ = 75 + 1.2816*9 = 86.5340

or you can directly find the score using function NORM.INV(0.90, 75, 9) = 86.5340

Lowest acceptable score for Grade B:

At top 20% = above 80% of the scores

Z score at p = 0.8 using excel = NORM.S.INV(0.8) =0.8416

Value of X = µ + z*σ = 75 + 0.8416*9 = 82.5746

Lowest acceptable score for Grade C:

At top 30% = above 70% of the scores

Z score at p = 0.7 using excel = NORM.S.INV(0.7) =0.5244

Value of X = µ + z*σ = 75 + 0.5244*9 = 79.7196

Lowest acceptable score for Grade D:

At top 40% = above 60% of the scores

Z score at p = 0.6 using excel = NORM.S.INV(0.6) =0.2533

Value of X = µ + z*σ = 75 + 0.2533*9 = 77.2801

Lowest acceptable score for Grade F:

Score below 77.2801 get Grade F