The central limit theorem (CLT)is considered to be an important result in statistics because
A)the CLT allows us to assume that the population distribution is approximately normal,provided n is reasonably large.
B)the CLT allows us to estimate the population mean without knowing the exact form of the population distribution,provided n is reasonably large.
C)the CLT allows us to construct confidence intervals for the population mean without knowing the exact form of the population distribution,provided n is reasonably large.
D)of all of these choices.

Question

Quizplus · Accepted Answer

The central limit theorem is crucial because it justifies the use of normal distribution approximations for sample means and other statistics, regardless of the population distribution, as long as the sample size is large enough. This enables estimation of population parameters and construction of confidence intervals without needing the population's exact distribution, making choices A, B, and C all correct applications of the CLT.

The Central Limit Theorem (CLT)is Considered to Be an Important