standard normal distribution

The standard normal distribution is a specific type of normal distribution, a probability density function that approximates the distribution of many random variables. It is characterized by a bell-shaped curve that is symmetric around its mean, which is the peak of the graph. The standard deviation determines the spread of the data; a smaller standard deviation results in a steeper curve, while a larger one creates a flatter curve.1

The standard normal distribution has a mean of 0 and a standard deviation of 1. This specific version is often used because any normal distribution can be converted to a standard normal distribution by rescaling its variables. This allows for easier comparison and analysis of different datasets. The formula for the normal distribution is given by (f(x) = \frac{1}{\sqrt{2\pi\sigma^{2}}}e^{-\frac{(x - \mu)^{2}}{2\sigma^{2}}}), where (\mu) is the mean and (\sigma) is the standard deviation.12