Normal approximation for the sample proportion (HSC SSCE Mathematics Extension 1): Flashcards

p̂ = x/n, ratio of successes to sample size.

It predicts larger group proportions from samples.

p̂ = number of successes / sample size.

Sample means approach a normal distribution as n increases.

n̂p ≥ 5 and n(1 - p̂) ≥ 5 must be met.

E(p̂) ≈ p̂, the expected sample proportion.

SD(p̂) = √(p̂(1-p̂)/n).

To convert p̂ to a z-score for probability calculations.

A z-score measures how many standard deviations a value is from the mean.

Predicting outcomes based on sample data.