Standard Normal Calculator

Calculate the probability density function value for the standard normal distribution (mean=0, SD=1) at a given z-value.

PDF phi(z)

0.05844094

PDF phi(-z)0.05844094
z-squared3.841600

PDF phi(z) vs Z-Value

सूत्र देखें →

सूत्र

## Standard Normal Distribution ### PDF Formula **phi(z) = (1 / sqrt(2*pi)) * e^(-z^2/2)** The standard normal distribution has mean 0 and standard deviation 1. It is the reference distribution for z-scores and hypothesis testing. The PDF is symmetric around z=0, meaning phi(z) = phi(-z). Common critical values: z = 1.645 (90%), 1.96 (95%), 2.576 (99%).

हल किया गया उदाहरण

Find the PDF value at z = 1.96 (the 95% critical value).

  1. 01phi(1.96) = (1 / sqrt(2*pi)) * e^(-1.96^2 / 2)
  2. 02= 0.39894 * e^(-1.9208)
  3. 03= 0.39894 * 0.14634
  4. 04= 0.05844