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 top 10% of students. What is the bottom cutoff for an A
Grade? Round your answer to the nearest whole number.
A)80
B)79
C)90
D)82

Question

Quizplus · Accepted Answer

To find the bottom cutoff for an A grade, which is given to the top 10% of students, we need to find the z-score that corresponds to the top 10% in a standard normal distribution. The z-score for the 90th percentile (top 10%) is approximately 1.28. Using the formula for converting z-scores to raw scores: X = μ + zσ, where μ is the mean, σ is the standard deviation, and z is the z-score, we get X = 70 + (1.28)(9) ≈ 81.52. Rounding to the nearest whole number gives us 82.

Solve the Problem. -Scores on a Test Are Approximately Normally Distributed with a Distributed