The Central Limit Theorem
Let X1,X2,...,Xn be a random sample from a distribution with mean μ and variance σ2. Then if n is sufficiently large, Xˉ has approximately a normal distribution with μXˉ=μ and σXˉ2=σ2/n. The larger the value of n, the better the approximation.
If n>30, the Central Limit Theorem can be used.
We have n=65>30. Then the Central Limit Theorem can be used
μXˉ=μ=20σXˉ2=σ2/n=400/65The sample mean Xˉ∼N(20,400/65)
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