Binomial to Normal Approximation
This page introduces the concept of converting binomial distribution to normal distribution in A Level Maths questions. It explains when and how to use the normal distribution as an approximation for binomial distribution.
The normal approximation to the binomial distribution is useful when dealing with large sample sizes and when the probability of success is close to 0.5.
Definition: The normal approximation to binomial A Level maths is used when n is large and p is close to 0.5, where n is the number of trials and p is the probability of success.
The conditions for using this approximation are:
- n is large (typically n > 30)
- np > 5 and n(1-p) > 5
When these conditions are met, a binomial distribution B(n, p) can be approximated by a normal distribution N(μ, σ²), where:
μ = np
σ² = np(1-p)
Highlight: This approximation is particularly useful for calculating probabilities in binomial distributions with large n, where direct calculation would be time-consuming.
The page provides examples of how to use this approximation in solving problems, demonstrating the binomial to normal approximation formula.
Example: If X ~ B(100, 0.3), approximate this using a normal distribution and calculate P(X > 35).
This approximation is a powerful tool in statistics, allowing for easier calculations and opening up the use of normal distribution techniques for binomial scenarios.
Vocabulary: Continuity correction is often applied when using the normal approximation to account for the discrete nature of the binomial distribution.
