Calcolatore Normale Standard
Calcola le probabilità della distribuzione normale standard con media 0 e deviazione 1.
PDF phi(z)
0.05844094
PDF phi(z) vs Z-Value
Formula
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%).
Esempio Risolto
Find the PDF value at z = 1.96 (the 95% critical value).
- 01phi(1.96) = (1 / sqrt(2*pi)) * e^(-1.96^2 / 2)
- 02= 0.39894 * e^(-1.9208)
- 03= 0.39894 * 0.14634
- 04= 0.05844
Domande Frequenti
Why is z = 1.96 special?
The area between -1.96 and 1.96 under the standard normal curve is approximately 0.95 (95%). This makes it the critical value for 95% confidence intervals and two-sided tests at alpha = 0.05.
What is the maximum value of the standard normal PDF?
The maximum occurs at z = 0, where phi(0) = 1/sqrt(2*pi) ≈ 0.3989. The curve decreases symmetrically from this peak.
How is the standard normal related to other normal distributions?
Any normal distribution N(mu, sigma) can be converted to the standard normal N(0,1) by the transformation Z = (X - mu) / sigma. This is why z-tables work for all normal distributions.
Impara