Answer:
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: