Introduction
Calculating normal distribution percentages is a crucial task in statistics, providing insights into the likelihood of events occurring within a given range. This article introduces a handy Normal Distribution Percentage Calculator, accompanied by an HTML and JavaScript code snippet for easy implementation.
How to Use
To utilize the Normal Distribution Percentage Calculator, follow these simple steps:
- Enter the mean (μ) and standard deviation (σ) in the designated input fields.
- Specify the range by inputting the lower and upper limits.
- Click the “Calculate” button to obtain the percentage of data within the specified range.
Formula
The calculation involves the cumulative distribution function (CDF) of the normal distribution. The formula is:
P(a < X < b) = \frac{1}{2} \left(1 + \text{erf}\left(\frac{b – \mu}{\sigma\sqrt{2}}\right) – \frac{1}{2} \left(1 + \text{erf}\left(\frac{a – \mu}{\sigma\sqrt{2}}\right)\right)
Here, erf represents the error function.
Example
Suppose we want to find the percentage of data between 80 and 100 in a normal distribution with a mean (μ) of 90 and a standard deviation (σ) of 5.
P(80 < X < 100) = \frac{1}{2} \left(1 + \text{erf}\left(\frac{100 – 90}{5\sqrt{2}}\right) – \frac{1}{2} \left(1 + \text{erf}\left(\frac{80 – 90}{5\sqrt{2}}\right)\right)
FAQs
Q1: What is the error function (erf)?
A1: The error function (erf) is a mathematical function that describes the probability of a Gaussian distribution falling within a certain range.
Q2: How accurate is the calculator’s calculation?
A2: The calculator uses precise formulas for normal distribution percentages, ensuring accurate results.
Conclusion
The Normal Distribution Percentage Calculator simplifies statistical calculations by providing accurate results based on the normal distribution. Whether you are a student or a professional dealing with statistical analysis, this tool proves invaluable in determining probabilities within specific data ranges.