A humanities professor assigns letter grades on a test according to the following scheme.
A: Top 8%
of scores
B: Scores below the top 8%
and above the bottom 58%
C: Scores below the top 42%
and above the bottom 22%
D: Scores below the top 78%
and above the bottom 7%
F: Bottom 7%
of scores
Scores on the test are normally distributed with a mean of 77.1
and a standard deviation of 7.4
. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.
To find the minimum score required for an A grade, we first need to find the z-score that corresponds to the top 8% of scores.
Using a z-table or calculator, we find that the z-score corresponding to the top 8% of scores is approximately 1.41.
Next, we use the z-score formula: z = (X - μ) / σ
where X is the score we are trying to find, μ is the mean (77.1), and σ is the standard deviation (7.4).
Plugging in the values, we get:
1.41 = (X - 77.1) / 7.4
Solving for X:
1.41 * 7.4 = X - 77.1
10.434 = X - 77.1
X = 87.534
Rounded to the nearest whole number, the minimum score required for an A grade is 88.