Question

GRADING ON A NORMAL CURVE – MR. SANDERSON MARKS HIS CLASS ON A NORMAL CURVE. THOSE WITH z-SCORES ABOVE 1.8 WILL RECEIVE AN A, THOSE BETWEEN 1.8 AND 1.1 WILL RECEIVE A B, THOSE BETWEEN 1.1 AND -1.2 WILL RECEIVE A C, THOSE BETWEEN -1.2 AND -1.9 WILL RECEIVE A D, AND THOSE UNDER -1.9 WILL RECEIVE AN F. FIND THE PERCENT OF GRADES THAT WILL BE A, B, C, D, AND F.

Answer 1

The probabilities from the Normal Curve must be obtained from tables or any informatic tool. It's not possible to be manually calculated.

Mr. Sanderson uses the z-scores to mark his class.

The points where he establishes the divisions between marks are:

1.8, 1.1, -1.2, and -1.9.

Determine the probabilities from the automatic tools:

P(z < 1.8) = 0.9640 = 96.40%

P(z < 1.1) = 0.8643 = 86.43%

P(z < -1.2) = 0.1151 = 11.51%

P(z < -1.9) = 0.0287 = 2.87%

Grade A is for those above 1.8, or:

P(z > 1.8) = 100% - 96.40% = 3.60%

Grade B is for those between 1.1 and 1.8, thus:

P(z < 1.8) - P(z < 1.1) = 96.40% - 86.43% = 9.97%

Grade C is for those between -1.2 and 1.1, thus:

P(z < 1.1) - P(z < -1.2) = 86.43% - 11.51% = 74.92%

Grade D is for those between -1.9 and -1.2, thus:

P(z < -1.2) - P(z < -1.9) = 11.51% = 11.51% - 2.87% = 8.64%

Finally, grade E is for those with a score less than -1.9:

P(z < -1.9) = 2.87%