Question

The scores on an economics examination are normally distributed with a mean of 69 and a standard deviation of 13. If the instructor assigns a grade of A to 13% of the class, what is the lowest score a student may have and still obtain an A?

Answer 1

To determine the lowest A score in the class with normally distributed exam scores, a z-score of 1.12, corresponding to the top 13%, is used. The score is then calculated to be approximately 84 using the z-score formula, considering the class mean of 69 and a standard deviation of 13.

Step-by-step explanation:

To find the lowest score a student may have and still obtain an A in a class where the scores are normally distributed with a mean of 69 and a standard deviation of 13, and where 13% of the class receives an A, we need to determine the z-score that corresponds to the top 13% of a normal distribution.

First, we look up the z-score that corresponds to the top 13% in a z-table or using a statistical software or calculator that can compute this percentile. This z-score happens to be approximately 1.12. We then use the z-score formula to solve for the score X that corresponds to this z-score:

Z = (X - μ) / σ

1.12 = (X - 69) / 13

Multiplying both sides by 13 gives us:

1.12 * 13 = X - 69

14.56 = X - 69

Adding 69 to both sides gives us the lowest A score:

X = 14.56 + 69

X = 83.56

Therefore, the lowest score a student can get and still receive an A is approximately 84 when rounded up to the nearest whole number since most grading scales use whole numbers.