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
To find the bottom cutoff for a D grade, we need to determine the z-score that corresponds to the 16th percentile.
Using a standard normal distribution table or a calculator, we find that the z-score corresponding to the 16th percentile is approximately -0.994.
The formula for calculating the z-score is:
z = (x - μ) / σ
Rearranging the formula to solve for x, we get:
x = z * σ + μ
Plugging in the values, we have:
x = -0.994 * 9 + 70
Calculating, we get:
x = 60.05
Rounding to the nearest whole number, the bottom cutoff for a D grade is 60.