Frequently Asked Questions
What is the standard normal distribution?
The standard normal has mean μ = 0 and standard deviation σ = 1. Any normal distribution can be converted to standard normal by the z-score transformation z = (x − μ) ÷ σ. Standard normal tables and z-scores are based on this distribution.
What is the difference between a z-score and a percentile?
A z-score is the standardized distance from the mean in standard-deviation units. A percentile is the cumulative probability Φ(z) expressed as a percentage. z = 1.28 corresponds to the 90th percentile; z = 1.96 to the 97.5th percentile.
Should I enter the variance or the standard deviation?
Enter the standard deviation σ (the square root of the variance). Entering the variance instead inflates every z by √σ and gives completely wrong probabilities. Double-check that σ > 0.
Can I use this for a sample mean?
Yes. If you want the probability that a sample mean falls below a threshold, use the standard error σ÷√n as the σ input. The sample mean follows a normal distribution with mean μ and standard deviation σ÷√n (by the Central Limit Theorem for large n).
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This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.