Since the central limit theorem states that a normal distribution of sample means will result from virtually any underlying distribution,all of the following are true except ________.
A)approximately 75% of the sample means will be between ±2 standard errors of μ
B)approximately 99% of the sample means will be between ±3 standard errors of μ
C)approximately 95% of the sample means will be between ±2 standard errors of μ
D)approximately 68% of the sample means will be between ±1 standard errors of μ

Question

Quizplus · Accepted Answer

The central limit theorem indeed implies that about 68% of the sample means will be within ±1 standard error of the population mean (μ), about 95% within ±2 standard errors, and about 99% within ±3 standard errors. Therefore, the statement that approximately 75% of the sample means will be between ±2 standard errors of μ is incorrect and does not align with the properties of the normal distribution as described by the central limit theorem.

Since the Central Limit Theorem States That a Normal Distribution