MCPCalc

Normal Distribution Calculator

Compute z-score, cumulative probability, percentile rank, and interval probability for a normal distribution.

Scratchpad (not saved)

What This Calculator Does

This calculator turns values into z-scores and then uses the normal CDF to report left-tail, right-tail, percentile, and interval probabilities. It is useful for standardized scores, threshold analysis, and quick approximations to many sampling models.

It combines Mean μ, Standard Deviation σ, Value x, Lower Bound to estimate Z-Score, P(X <= x), Percentile Rank.

Formula & Method

Core equations: z=\frac{x-\mu}{\sigma},\quad P(X\le x)=\Phi(z),\quad P(a\le X\le b)=\Phi(z_b)-\Phi(z_a).

Notation used in the formulas: R = Z-Score; x_{1} = Mean μ; x_{2} = Standard Deviation σ; x_{3} = Value x; x_{4} = Lower Bound; x_{5} = Upper Bound.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when data are approximately bell-shaped or when another model is well-approximated by a normal distribution and you need probability mass below, above, or between target values.

Inputs Used

  • Mean μ: Used directly in the calculation.
  • Standard Deviation σ: Used directly in the calculation.
  • Value x: Used directly in the calculation.
  • Lower Bound: Used directly in the calculation.
  • Upper Bound: Used directly in the calculation.

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