Calculadora de Distribución Normal Gratis
Calcula probabilidades bajo la curva normal. Ingresa media, desviación estándar y rango de valores.
Puntuación Z
0.500000
Z-Score vs Value (x)
Fórmula
## How to Use the Normal Distribution ### PDF Formula **f(x) = (1 / (sigma * sqrt(2*pi))) * e^(-0.5 * ((x - mu)/sigma)^2)** The normal (Gaussian) distribution is the most important continuous distribution in statistics. It is defined by its mean (mu) and standard deviation (sigma). The z-score standardizes any value to units of standard deviations from the mean.
Ejemplo Resuelto
Test scores have mean 70 and SD 10. Find the z-score and PDF for a score of 75.
- 01Z = (75 - 70) / 10 = 0.5
- 02The score is 0.5 standard deviations above the mean
- 03PDF = (1 / (10 * sqrt(2*pi))) * e^(-0.5 * 0.25)
- 04= 0.03989 * 0.8825 = 0.03521
- 05Variance = 10^2 = 100
Preguntas Frecuentes
What does the 68-95-99.7 rule mean?
About 68% of data falls within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3. This empirical rule applies to any normal distribution.
What is the difference between PDF and CDF?
The PDF gives the relative likelihood at a point (height of the curve). The CDF gives the cumulative probability up to that point (area under the curve to the left). The PDF value itself is not a probability.
Why is the normal distribution so important?
The Central Limit Theorem states that the sum (or mean) of many independent random variables tends toward a normal distribution, regardless of the underlying distribution. This makes it foundational for statistical inference.
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