## If a random sample of size nequals=6 is taken from a​ population, what is required in order to say that the sampling distribution of x overb

Question

If a random sample of size nequals=6 is taken from a​ population, what is required in order to say that the sampling distribution of x overbarx is approximately​ normal?

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1 week 2021-11-21T10:57:38+00:00 1 Answer 0 views 0

In order to satisfy this distribution we need that each observation on this case comes from a normal distribution, because since the sample size is not large enough we can’t apply the central limit theorem.

Step-by-step explanation:

For this case we have that the sample size is n =6

The sample man is defined as :

And we want a normal distribution for the sample mean

In order to satisfy this distribution we need that each observation on this case comes from a normal distribution, because since the sample size is not large enough we can’t apply the central limit theorem.

So for this case we need to satisfy the following condition:

Because if we find the parameters we got:

And the deviation would be:

And we satisfy the condition: