The sampling distribution of $\bar { X }$
must be a normal distribution with mean = 0 and standard deviation = 1.

Question

The sampling distribution of $\bar { X }$ 
must be a normal distribution with mean = 0 and standard deviation = 1.

Quizplus · Accepted Answer

The sampling distribution of $\bar { X }$ does not have a fixed mean and standard deviation. Its mean and standard deviation depend on the population from which the samples are drawn and the sample size. However, as per the Central Limit Theorem, as the sample size increases, the sampling distribution of $\bar { X }$ approaches a normal distribution with mean = population mean and standard deviation = $\frac { \sigma  }{ \sqrt { n }  }$, where $\sigma$ is the population standard deviation and n is the sample size.

The Sampling Distribution Of Xˉ\bar { X }Xˉ Must Be a Normal Distribution with Mean = 0 and a Normal

The Sampling Distribution Of $\bar { X }$ Must Be a Normal Distribution with Mean = 0 and a Normal