Scores on a test are approximately normally distributed with a men of 70 and a standard deviation of 9. The teacher wants to give A's to the top 10% of students. What is the bottom cutoff for an A grade? Please round answer to the nearest whole number

To find the bottom cutoff for an A grade, you need to determine the score below which only the top 10% of students will fall.

Since the scores on the test are approximately normally distributed with a mean (μ) of 70 and a standard deviation (σ) of 9, you can use the Z-score formula to find the cutoff point.

The formula to calculate the Z-score is:
Z = (X - μ) / σ

Where:
Z is the Z-score,
X is the raw score,
μ is the mean, and
σ is the standard deviation.

To find the Z-score representing the top 10%, you can use the Z-score table or a statistical calculator. The Z-score representing the top 10% is approximately 1.28.

Now, rearrange the Z-score formula to solve for X:
X = Z * σ + μ

Substituting the values into the formula:
X = 1.28 * 9 + 70
X = 80.92

To round the answer to the nearest whole number:
X ≈ 81

Therefore, the bottom cutoff for an A grade is approximately 81.

82