From past history, the scores on a statistics test are normally distributed with a mean of 70% and a standard deviation of 5%. To earn a "C" on the test, a student must be in the top 25% of the class. What should a student score to receive a "C"?
A) 77.21
B) 73.37
C) 73.96
D) 76.90

Question

Quizplus · Accepted Answer

To find the score that corresponds to the top 25% of the class, we look for the z-score that corresponds to the 75th percentile (since the top 25% means the lowest score in that range is at the 75th percentile of all scores). The z-score for the 75th percentile is approximately 0.674 (from z-tables or a standard normal distribution calculator). Using the formula for converting z-scores to raw scores: X = μ + Zσ, where X is the raw score, μ is the mean, Z is the z-score, and σ is the standard deviation, we get X = 70 + (0.674)(5) = 70 + 3.37 = 73.37.

From Past History, the Scores on a Statistics Test Are