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The standard score is a very useful statistic because it allows us to compute the probability of a score ensuing within our normal distribution

A $Z\mathit{-}$score is a numerical measurement that describes a value's relationship to the mean of a group of values. $Z\mathit{-}$score is calculated in terms of standard deviation from the mean. If a $Z-$score is $\mathit{0}$, it denotes that the data point's score is identical to the mean score. A $Z-$score of $1.0$would indicate a value that is one standard deviation from the mean. $Z-$scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score showing it is below the mean. The formula for calculating a $z-$score is $z=(x-\mathrm{μ})/\mathrm{σ}$, where $x$is the raw score, $\mathrm{μ}$is the population mean, and $\mathrm{σ}$is the population standard deviation.