Question

Final averages are typically approximately normally distributed with a mean of 74 and a standard deviation of 12. your professor says that

the top 10 percent of class will receive A,
the next 20 percent B,
the next 40 percent C,
the next 20 percent D,
and the bottom 10 percent F.
1.What average must you exceed to obtain an A?
2.What average must you exceed to receive a grade better than a C?
3.What average must you exceed to obtain a D?

Answer 1

To obtain an A, you must exceed an average of 88.36. To receive a grade better than a C, you must exceed an average of 70.5. To obtain a D, you must exceed an average of 62.32.

Step-by-step explanation:

To determine the average needed to obtain an A, we need to find the cutoff point that separates the top 10% of the class from the rest. We can use the z-score formula: z = (x - mean) / standard deviation. Looking up the z-score corresponding to the top 10% in a standard normal distribution table, we find a z-score of 1.28.

Using the formula, 1.28 = (x - 74) / 12, we can solve for x and find that x ≈ 88.36. Therefore, you must exceed an average of 88.36 to obtain an A.

To receive a grade better than a C, we need to find the average that separates the top 60% from the bottom 40% of the class. This corresponds to a z-score of -0.25. Using the formula, -0.25 = (x - 74) / 12, we can solve for x and find that x ≈ 70.5. Therefore, you must exceed an average of 70.5 to receive a grade better than a C.

To obtain a D, we need to find the average that separates the top 80% from the bottom 20% of the class. This corresponds to a z-score of -0.84. Using the formula, -0.84 = (x - 74) / 12, we can solve for x and find that x ≈ 62.32. Therefore, you must exceed an average of 62.32 to obtain a D.