A 400-student lecture in introductory statistics conducted by a tenured professor breaks into 20 sections of 20 students for problem sessions run by helpful graduate assistants that give weekly quizzes to lighten the mood.The graduate assistants determine their section averages for their quiz each week and compare the numbers.Which of these statements is best?
A)The standard deviation of the section averages should approach the overall standard deviation.
B)A graduate assistant whose section quiz average falls outside three sigma limits should be replaced.
C)For any given week, the section averages should be normally distributed.
D)95.5% of the section averages should fall within three standard deviations of the overall average.

Question

Quizplus · Accepted Answer

DC) The Central Limit Theorem suggests that, given a sufficiently large sample size, the distribution of the sample means (in this case, section averages) will be approximately normally distributed, regardless of the shape of the population distribution.D) According to the empirical rule (or 68-95-99.7 rule), for a normally distributed dataset, approximately 95.5% of the values lie within three standard deviations of the mean. This applies to the distribution of section averages if they are normally distributed.

A 400-Student Lecture in Introductory Statistics Conducted by a Tenured