In a large lecture class, the professor announced that the scores on a recent exam were normally distributed with a range from 51 to 87. Using the Empirical Rule μ ± 3σ to estimate σ, how many students would you need to sample to estimate the true mean score for the class with 90 percent confidence and an error of ±2?
A)About 17 students
B)About 35 students
C)About 188 students
D)About 25 students

Question

Quizplus · Accepted Answer

First, calculate the standard deviation (σ) using the range and the Empirical Rule. The range is 87 - 51 = 36, which covers 6σ (from -3σ to +3σ). Therefore, σ = 36/6 = 6. To estimate the true mean with 90% confidence and an error of ±2, use the formula for the sample size n = (Z*σ/E)^2, where Z is the Z-score for 90% confidence (approximately 1.645) and E is the margin of error (2). Plugging in the values gives n = (1.645*6/2)^2 ≈ 25. Hence, about 25 students would need to be sampled.

In a Large Lecture Class, the Professor Announced That the Scores