Normal Approximation to B(n,p)

Normal Approximation to B(n,p)

• Normal Approximation to Binomial Distribution:
  • Method used to estimate binomial probabilities utilising a normal distribution.
  • Applied when sample size is large and the probability of success is neither close to 0 or 1.
  • Justification largely comes from the Central Limit Theorem.
• Central Limit Theorem:
  • Stipulates that a sum of a large number of independent and identically distributed variables will approximate a normal distribution.
• Characteristics of Normal Approximation:
  • Normal distribution has a mean (μ) of np and a variance (σ^2) of np(1-p).
• Application of Continuity Correction in Normal Approximation:
  • Probability of X falling in a given range found by considering area under normal curve that corresponds to range.
  • Calculation requires addition or subtraction of 0.5 to boundaries of the range to bridge gap between discrete and continuous probability distributions.
• Significance of Normal Approximation:
  • Simplifies computations significantly.
  • Provides a practical way of estimating binomial probabilities for large samples.
  • Acts as a valuable tool in statistical analysis.