Sampling from a normally distributed population.
What can we conclude when sampling from a normally distributed population? In other words, what can we conclude about samples drawn from a normally distributed population with mean equal to μ and standard deviation equal to σ ?
The followings hold true:
a.
The mean of x̄ or μx̄ is equal to the mean of the population or μ.
μx̄ = μ
The standard deviation of x̄ or σx̄ is equal to σ/√n assuming of course n/N ≤ 0.05
$$ \sigma_{\overline{x}} = \frac{\sigma }{\sqrt{n} } $$b. No matter what the value of n is, the shape of the sampling distribution of x̄ is also normally distributed.
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