What is normal distribution?

The normal (Gaussian) distribution is a symmetric, bell-shaped curve where data clusters around the mean. It's defined by two parameters: mean (μ) and standard deviation (σ).

What is the 68-95-99.7 rule?

In a normal distribution: ~68% of data falls within ±1σ, ~95% within ±2σ, and ~99.7% within ±3σ of the mean. This is also called the empirical rule.

P(X < x) is the cumulative probability - the area under the curve to the left of x. It represents the probability of observing a value less than x.

What is P(a < X < b)?

P(a < X < b) is the probability of X falling between a and b. Calculate as P(X < b) - P(X < a).

When is data normally distributed?

Many natural phenomena approximate normal distribution: heights, test scores, measurement errors. The Central Limit Theorem states that sample means tend toward normal distribution regardless of population shape.

Normal Distribution Calculator

Calculate probabilities for the Gaussian (bell curve) distribution.

Distribution Parameters

Mean (μ)

Center of the distribution

Standard Deviation (σ)

Spread of the distribution

Calculate

X Value

Probability

0 %

P(X < 85)

Distribution Curve

Z-Score (x₁)

Probability

1 in X

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