qnorm05

qnorm05 is a shorthand term used in statistics to denote the 5th percentile, or the quantile at probability 0.05, of the normal distribution. In its standard form, it refers to the lower tail value of a standard normal distribution, meaning the value x for which P(X ≤ x) = 0.05 when X follows a N(0,1) distribution. The corresponding z-score is approximately -1.644853627.

For a normal distribution with mean mu and standard deviation sigma, the 5th percentile is given by qnorm05(mu, sigma) = mu + sigma * z0.05, where z0.05 ≈ -1.644853627. Equivalently, qnorm05 is the inverse cumulative distribution function (the percent point function) evaluated at p = 0.05. This provides a threshold below which about 5% of observations are expected under the given normal model.

Interpretation and usage: qnorm05 defines a lower bound used in risk assessment, quality control, and one-sided statistical procedures. It is the value such that only 5% of the distribution lies below it. In practice, software implementations often compute this as qnorm(0.05) or qnorm(0.05, mean, sd). The term qnorm05 is an informal shorthand rather than a universal built-in function, and practitioners may encounter it in notes, tutorials, or custom scripts. Related concepts include z-scores, percentile thresholds, and other quantiles such as the 95th percentile (qnorm95) for the upper tail.