On a recent English exam,if 94% of scores fell above 65 points and the standard deviation is 7.5,find the mean score (assuming the Normal model is appropriate).
A)7.05
B)-53.34
C)76.66
D)61.75
E)72.5

Question

Quizplus · Accepted Answer

Since 94% of scores fell above 65 points, we can assume that 6% of scores were below or equal to 65 points. Using the standard normal distribution table, we can find the z-score that corresponds to the 6th percentile (i.e. the value that separates the bottom 6% from the top 94%). This z-score is approximately -1.55.
We can use the formula z = (x - μ) / σ, where z is the z-score, x is the raw score, μ is the mean score, and σ is the standard deviation. Rearranging, we get x = σz + μ.
Plugging in the given values, we get 65 = 7.5(-1.55) + μ, which simplifies to μ ≈ 76.67. Therefore, the mean score is approximately 76.67, which is closest to option C (76.66).

On a Recent English Exam,if 94% of Scores Fell Above