Distribution of z-scores

Calculating a z-score from a value, x, is called standardising it.

standardised value,   

If X has a normal distribution, then Z has a standard normal distribution with mean µ = 0 and standard deviation σ = 1.

Probabilities for the standard normal distribution

After translating a probability about X into one about a z-score, it is easier to evaluate it.

Areas under the standard normal curve can be evaluated in Excel and most statistical programs. Statistical tables can also be used (see later).