Lower and Upper Bounds of a Normal Distribution Calculator
Lower and upper bounds of a normal distribution are crucial in statistics, helping us understand the spread of data and make informed decisions. Our calculator simplifies this process, providing instant results and a detailed guide.
- Enter the mean (μ) and standard deviation (σ) of your data.
- Select your desired confidence interval.
- Click ‘Calculate’ to see your results.
The formula for calculating the bounds is:
Z = (X – μ) / σ
Where X is the value at the desired confidence level, μ is the mean, σ is the standard deviation, and Z is the Z-score. We use the inverse of the standard normal cumulative distribution function (CDF) to find X.
| Confidence Interval | Z-score | Lower Bound | Upper Bound |
|---|---|---|---|
| 90% | 1.645 | -1.645 | 1.645 |
| 95% | 1.96 | -1.96 | 1.96 |
| 99% | 2.576 | -2.576 | 2.576 |
- Always use the appropriate confidence interval for your analysis.
- Understand the limitations of the normal distribution assumption.
- Consider using bootstrapping or other methods for small sample sizes.
What is a normal distribution?
A normal distribution, also known as a Gaussian distribution, is a continuous probability distribution that is symmetric about its mean and has a bell-shaped curve.
For more information, see these authoritative sources:
NIST Engineering Statistics Handbook StackExchange – Confidence Interval vs Margin of Error