The number of possible samples which can be selected without replacement is
(Nn)=n!⋅(N−n)!N!==3!⋅3!6!=2⋅34⋅5⋅6=20.
Population mean:
μ=63+5+7+9+11+13=8.
Population variance:
σ2=∑(xi−μ)2⋅P(xi),
X−μ=={3−8,5−8,7−8,9−8,11−8,13−8}=
={−5,−3,−1,1,3,5},
σ2=(−5)2⋅61+(−3)2⋅61++(−1)2⋅61+12⋅61+32⋅61+52⋅61=11.667.
Mean of the sampling distribution of sample means:
μxˉ=μ=8.
Variance of the sampling distribution of sample means:
σxˉ2=nσ2=311.667=3.889.
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