About this calculator
Normal Distribution Calculator is a professional statistical analysis tool for calculating probabilities, quantiles and statistics of the normal distribution (Gaussian distribution). The normal distribution is the most important continuous probability distribution, which is a bell-shaped curve and is completely determined by the mean μ and the standard deviation σ. Many random variables in nature and social phenomena approximately obey a normal distribution, such as height, weight, test scores, measurement errors, etc. This calculator supports standard normal distribution and general normal distribution, and can calculate probability, quantiles, confidence intervals, etc. It is an essential tool for statistical analysis and data processing.
What it calculates
Normal distribution calculator is based on the complete Chinese reference article for this calculator. It explains what the tool calculates, when to use it, and how the result relates to the underlying formula.
Formula
Use the formula shown by Normal distribution calculator together with the values entered in the calculator. Keep units consistent and check any restrictions before interpreting the answer.
- Identify the formula used by the calculator.
- Substitute the input values carefully.
- Simplify or interpret the result with the correct units.
Inputs
Enter the required values for Normal distribution calculator. Use numeric inputs where requested, keep variable names consistent, and review the selected unit or calculation mode before calculating.
- Required numeric values.
- Relevant units or variable names.
- Calculation mode or target value when available.
Example
A typical example uses simple values so you can compare the input, formula, and output. This helps verify that the calculator is being used correctly.
| Step | What to check | Purpose |
|---|---|---|
| 1 | Enter sample values | Confirm how Normal distribution calculator reads inputs |
| 2 | Review the formula | Understand the calculation method |
| 3 | Compare the result | Use the answer correctly |
How to interpret the result
The result should be read together with the formula, input values, and any displayed calculation steps. If the calculator shows multiple values, compare each label before using the answer.
Common mistakes
Most mistakes come from missing units, entering values in the wrong field, or ignoring formula restrictions. Recheck the inputs if the result looks unexpected.
- Check units and signs.
- Do not leave required inputs blank.
- Confirm that the formula conditions are satisfied.
How to use
Use the normal distribution calculator:
1. Select a distribution type: • Standard normal distribution (μ=0, σ=1) • General normal distribution (customized μ and σ) 2. Enter parameters: • Mean μ • Standard deviation σ (σ>0) 3. Select the calculation type: • P(X<x): Probability of being less than x • P(X>x): Probability greater than x • P(a<X<b): interval probability • Quantile: Find the value of x given the probability 4. Enter the value 5. View results and distribution plots
Main features
• Two-way calculation: probability → quantile, quantile → probability • Standardization: Automatic conversion to standard normal distribution • Distribution plots: probability density curves and cumulative distributions • Confidence Intervals: Calculate common confidence intervals • Z-score: Calculates the standardized score • Percentile: Calculate any percentile • Normality test: provides test methods • Totally free: unlimited use
Use cases
• Statistical inference: hypothesis testing and confidence intervals • Quality Control: Process Capability Analysis • Exam Analysis: Score Distribution and Ranking • Risk assessment: VaR calculation • Data analysis: normality test • Scientific research: experimental data analysis • Financial Analysis: Yield Distribution • Teaching Demonstration: Explaining the Normal Distribution