Free 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
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%).
Example Calculation
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
Frequently Asked Questions
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Understanding the Normal Distribution
Learn what the normal distribution is, why it matters in statistics, and how to use the bell curve for probability calculations, z-scores, and real-world data analysis.