What does this mean exactly?
I'm a bit confused about the part with z-score. It seems to be important when testing hypothesis.
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The notation '$X_k \in N(\mu,\sigma)$' in your source means that the random variable $X_k$ has a normal distribution with mean $\mu$ and standard deviation $\sigma$. The second symbol in $N(\cdot,\cdot)$ denotes the standard deviation, NOT the variance. This was brought to my attention by @Dilip Sarwate (see comment below).
It is more common to see the notation '$Y \sim N(u,\sigma^2)$' where the symbol '$\sim$' is prefered to '$\in$', which is more relevant to indicate membership of an element in a set, and where the second symbol in $N(\cdot,\cdot)$ denotes the variance. However, some softwares/programming languages also use standard deviation instead of variance as the second parameter (e.g. functions
[dpqr]norm in R).