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Normal Distribution Calculator

Find the cumulative probability P(X ≤ x) for a normal distribution given any mean, standard deviation, and x value. Useful for statistics students, researchers, and engineers working with continuous random variables.

Mean (μ)

Standard Deviation (σ)

X Value

Decimal Places

Fill in the required fields to see your result.

Statistics

Confidence Interval Calculator

Compute the lower and upper bounds of a confidence interval for a population mean using a sample mean, the standard error of that mean, and a critical z-value (1.645 / 1.96 / 2.576 for 90% / 95% / 99% confidence). This is the standard way to report uncertainty around survey results, lab measurements, or any sample-based estimate.

Sample Mean

Standard Error

Z-Value

Fill in the required fields to see your result.

Key differences

	Normal Distribution Calculator	Confidence Interval Calculator
Category	Statistics	Statistics
Inputs required	4	3
Result	Probability	Lower Bound
What it does	Find the cumulative probability P(X ≤ x) for a normal distribution given any mean, standard deviation, and x value. Useful for statistics students, researchers, and engineers working with continuous random variables.	Compute the lower and upper bounds of a confidence interval for a population mean using a sample mean, the standard error of that mean, and a critical z-value (1.645 / 1.96 / 2.576 for 90% / 95% / 99% confidence). This is the standard way to report uncertainty around survey results, lab measurements, or any sample-based estimate.