Asimple random sample of size nequals57 is obtained from a population with muequals69 and sigmaequals2. does the population need to be normally distributed for the sampling distribution of x overbar to be approximately normally distributed? why? what is the sampling distribution of x overbar?

The population does not need to be normally distributed for the sampling distribution of to be approximately normally distributed. Because of the central limit theorem. The sampling distribution of is approximately normal.

Step-by-step explanation:

We have a random sample of size from a population with and . Because n is large enough (i.e., n > 30) and and are both finite, we can apply the central limit theorem that tell us that the sampling distribution of is approximatelly normally distributed, this independently of the distribution of the random sample. is asymptotically normally distributed is another way to state this.

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