Probability Distributions
Visualize Normal and Binomial distributions.
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About this Distribution
The Normal Distribution (or Gaussian) is a continuous probability distribution that is symmetric about the mean. It shows that data near the mean are more frequent in occurrence than data far from the mean.
- Mean (μ): The center of the distribution.
- Standard Deviation (σ): Measure of the amount of variation or dispersion.
Probability Distribution Guide Guide
How to Use
- 1Select the distribution type: Normal (Gaussian) or Binomial.
- 2For Normal: Enter Mean (μ) and Standard Deviation (σ).
- 3For Binomial: Enter Number of Trials (n) and Probability of Success (p).
- 4Calculate probabilities for specific values (X).
Formula & Logic
The Binomial probability formula calculates the likelihood of getting exactly x successes in n independent trials. The Normal distribution uses a probability density function defined by mean and standard deviation.
Practical Applications
Quality Testing
Estimate the probability of a certain number of defective items in a production batch (Binomial).
Test Scores
Analyze student performance assuming grades follow a bell curve (Normal Distribution).
Risk Analysis
Model financial returns or insurance risks using normal distribution assumptions.
Frequently Asked Questions
Q.What is a Normal Distribution?
Also known as the bell curve, it is a symmetric probability distribution where most observations cluster around the central peak (mean).
Q.What is a Z-Score?
A Z-score describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean.
Q.When should I use the Binomial Distribution?
Use it when there are a fixed number of trials, each trial has only two possible outcomes (success/failure), and the probability of success is constant.