The scores on an Economics examination are normally distributed with a mean of 74 and a standard deviation of 11. If the instructor assigns a grade of A to 10% of the class, what is the lowest score (rounded to the nearest integer) a student may have and still obtain an A?
A) 86
B) 82
C) 89
D) 71
E) 80

Question

Quizplus · Accepted Answer

To find the lowest score for an A (top 10%), we use the Z-score formula for the 90th percentile in a normal distribution. The Z-score corresponding to the 90th percentile is approximately 1.28. Using the formula: Z = (X - μ) / σ, where X is the score, μ is the mean (74), and σ is the standard deviation (11), we solve for X: 1.28 = (X - 74) / 11. Solving for X gives us a score of approximately 88.08. Rounding to the nearest integer, the lowest score for an A is 89.

The Scores on an Economics Examination Are Normally Distributed with a Mean