Probability Distributions: Types, Applications, and Calculations
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Probability Distributions
Types of Probability Distributions
Normal Distribution
- Used to model continuous data
- Examples: Heights of people, scientific measurements, test scores
Binomial Distribution
- Used to model discrete data with two possible outcomes
- Examples: Number of heads in a coin toss, number of successes in a series of trials
Poisson Distribution
- Used to model the number of events occurring in a fixed interval of time or space
- Examples: Number of phone calls received per hour, number of earthquakes per year
Applications of Probability Distributions
- Sales success
- Launch of new products
- Bidding for contracts
- Quality control
- Hiring staff
- Experimental trials
Calculating Probabilities
Normal Distribution
- Use a calculator or statistical software
- Formula: P(X < x) = Φ((x - μ) / σ)
Binomial Distribution
- Use a calculator or statistical software
- Formula: P(X = x) = (n! / (x!(n-x)!)) * p^x * (1-p)^(n-x)
Poisson Distribution
- Use a calculator or statistical software
- Formula: P(X = x) = (e^-λ * λ^x) / x!