Normal Distribution Probability Calculator
This calculator helps find probabilities for normally distributed data. It's used in statistics, quality control, and risk analysis to determine the likelihood of events occurring within specific ranges in a normal distribution curve.
FAQs
What is normal distribution?
Normal distribution is a bell-shaped probability pattern where data is symmetrically distributed around the mean. About 68% of values fall within 1 standard deviation, 95% within 2 deviations, and 99.7% within 3 deviations. It's fundamental in statistics for natural phenomena and measurement errors.
How to interpret results?
The result shows the probability of a random variable falling between your specified bounds. A 0.25 probability means 25% chance. Values range 0-1. Use it to assess likelihood of outcomes in quality control, social sciences, and financial risk modeling.
What if data isn't normal?
This calculator assumes normality. For non-normal data, consider transformations or non-parametric methods. Results may be inaccurate for skewed distributions. Check normality using histograms or statistical tests before using this tool.
Difference between Z-score and raw score?
Z-scores standardize values by measuring deviations from mean in SD units. Raw scores are original measurements. The calculator converts raw scores to Z-scores using (X-μ)/σ formula when you input mean and SD.
Can I calculate tail probabilities?
Yes. For left tail, set upper bound to very low value. For right tail, set lower bound to very high value. Alternatively, use -infinity (practical limit: -5) or +infinity (+5) as bounds for extreme probabilities.