Solve the problem
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 too 10% of students, B’s to the next 25%,, C’s to the next 40%, D’s to the next 16% and F’s to the bottom 9%. What is the bottom cutoff for a grade D? Round your answer to the nearest whole number
To find the bottom cutoff for a grade D, we need to find the z-score corresponding to the 16th percentile.
Using a standard normal distribution table, we find that the z-score corresponding to the 16th percentile is approximately -0.994.
We can use the formula for the z-score to find the cutoff value:
z = (x - μ) / σ
Solving for x, we have:
x = z * σ + μ
Substituting the values given:
x = -0.994 * 9 + 70
x = -8.946 + 70
x = 61.054
Rounding this value to the nearest whole number, the bottom cutoff for a grade D is 61.