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 μ_{x̄} is equal to the mean of the population or μ.
μ_{x̄ = }μ
The standard deviation of x̄ or σ_{x̄} 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.
Aug 16, 22 04:10 AM