Calculate Normal Distribution by Hand
Calculating normal distribution by hand is a fundamental skill in statistics. It helps understand and interpret data, make informed decisions, and communicate findings effectively.
- Enter the mean (μ), standard deviation (σ), and z-score values.
- Click ‘Calculate’.
- View the result and chart below.
The formula to calculate the z-score is: Z = (X – μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation. The calculator uses this formula to find the corresponding probability.
| Z-score | Cumulative Probability |
|---|
- Understand the shape of the normal distribution curve.
- Interpret z-scores correctly: a z-score of 0 indicates the mean, while a z-score of 1 indicates one standard deviation above the mean.
- Use the empirical rule (68-95-99.7 rule) to estimate probabilities quickly.
What is the difference between a normal distribution and a standard normal distribution?
A normal distribution has a mean of 0 and a standard deviation of 1. A standard normal distribution is a normal distribution that has been standardized to have a mean of 0 and a standard deviation of 1.
Learn more about z-scores from this authoritative source.
Explore normal distribution on Khan Academy.