Normal Distribution Calculator
The Normal Distribution (also known as Gaussian distribution) is one of the most important probability distributions in statistics. It forms a symmetric bell-shaped curve, with the majority of observations clustering around the mean. This calculator helps you:
- Calculate probabilities for specific values (using PDF and CDF)
- Find critical values for given probabilities
- Convert between raw scores and standardized Z-scores
- Visualize probability distributions
Key Properties:
- Symmetric around the mean (μ)
- 68% of data falls within ±1 standard deviation
- 95% within ±2 standard deviations
- 99.7% within ±3 standard deviations
Common Applications:
Finance:
- Stock return distributions
- Risk assessment models
- Option pricing
- Portfolio analysis
Other Fields:
- Quality control measurements
- Natural phenomena modeling
- Experimental error analysis
- Population distributions
Calculation Type
Distribution Parameters
Important Notes:
- Standard deviation must be positive
- For a standard normal distribution, use mean = 0 and standard deviation = 1
- Z-scores show how many standard deviations a value is from the mean
- The probability density function (PDF) shows the relative likelihood of a specific value
- The cumulative distribution function (CDF) shows the probability of a value less than or equal to X