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!

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