# Normal Distribution Calculator Calculate z-scores, cumulative probability, tail probability, and interval probability for a normal distribution > Canonical page: https://elysiatools.com/en/tools/normal-distribution-calculator - **Category:** Math & Numbers - **Keywords:** normal distribution, probability, z score, percentile, statistics, calculator ## Overview The Normal Distribution Calculator allows you to perform statistical analysis by calculating z-scores, cumulative probabilities, and interval probabilities based on your specific mean and standard deviation parameters. ## Inputs - **Raw Value** (text): e.g. 85 - **Mean** (text): e.g. 75 - **Standard Deviation** (text): e.g. 10 - **Lower Bound (Optional)** (text): Optional interval lower bound - **Upper Bound (Optional)** (text): Optional interval upper bound - **Decimal Precision** (number) ## When to use - When you need to determine the percentile rank of a specific data point within a normal distribution. - When you want to calculate the probability of a value falling within a specific range or interval. - When you are performing statistical hypothesis testing and need to find tail probabilities. ## How it works - Enter the raw value, the population mean, and the standard deviation into the respective fields. - Optionally, provide lower and upper bounds if you need to calculate the probability of a value falling within a specific interval. - Set your desired decimal precision to ensure the output meets your reporting requirements. - Click calculate to receive the z-score, cumulative probability, and relevant tail or interval probabilities. ## Use cases - Academic grading: Determining the percentage of students who scored above or below a certain threshold. - Quality control: Calculating the probability that a manufactured part falls within acceptable tolerance limits. - Financial analysis: Estimating the likelihood of asset returns falling within a specific range based on historical volatility. ## Frequently asked questions ### What is a z-score? A z-score represents the number of standard deviations a data point is from the mean of the distribution. ### What does cumulative probability measure? It measures the probability that a random variable will take a value less than or equal to the specified raw value. ### Can I calculate probabilities for ranges? Yes, by entering values into the Lower Bound and Upper Bound fields, the tool calculates the probability of a value falling within that range. ### What is the default decimal precision? The tool defaults to 4 decimal places, but you can adjust this between 0 and 10 based on your needs. ### Is this tool suitable for non-normal distributions? 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