The scores for a recent English exam can be represented by the Normal model N(71,7.0).What score would you expect to be unusually high for this exam?
A)50
B)64
C)74.5
D)92
E)78

Question

Quizplus · Accepted Answer

To find a score that is unusually high, we need to look for values that are several standard deviations above the mean. To do this, we can use the z-score formula:

z = (x - μ) / σ

where x is the score we are interested in, μ is the mean, and σ is the standard deviation.

For an unusually high score, we want a z-score that is greater than 2 (since this corresponds to being more than 2 standard deviations above the mean). We can rearrange the formula to solve for x:

x = z * σ + μ

Substituting z = 2 and σ = 7.0, we get:

x = 2 * 7.0 + 71 = 85

Therefore, an unusually high score for this exam would be 85 or higher. The closest choice to this value is D: 92, which is more than 2.5 standard deviations above the mean and would be considered very high.

The Scores for a Recent English Exam Can Be Represented