Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A’s to the top 10% of students, AB’s to the next 25%, C’s to the next 40%, D’s to the nest 16%, and F’s to the bottom 9%. What is the bottom cutoff for a D grade? Round your answer to the nearest whole number
A.58
B.56
C.65
To find the bottom cutoff for a D grade, we need to find the score that corresponds to the bottom 16% of students.
Using the z-score formula, we can calculate the z-score for the bottom 16%:
z = (X - μ) / σ
z = (X - 70) / 9
To find the cutoff score, we need to find the value of X that corresponds to a z-score of -0.95 (the z-score for the 16th percentile).
-0.95 = (X - 70) / 9
Multiply both sides by 9:
-8.55 = X - 70
X = -8.55 + 70
X = 61.45
Rounded to the nearest whole number, the bottom cutoff for a D grade is 61.
Therefore, the answer is C.65.