Continuity Correction

When approximating a discrete random variable (taking integer values k) with a continuous distribution, the discrete val

Normal Distribution

Distribution of Sample Mean

If X ~ N(μ, σ²), then the sample mean X̄ from n independent observations follows X̄ ~ N(μ, σ²/n). The standard error of

Normal Distribution

Normal Approximation to Binomial

For large n, a binomial distribution B(n, p) can be approximated by a normal distribution N(np, np(1-p)), provided np ≥

Normal Distribution

6.1: Normal Distribution

A continuous probability distribution with probability density function determined by mean μ and standard deviation σ, d

Normal Distribution

6.1: Normal Distribution

The normal distribution N(μ, σ²) has: (1) a bell-shaped, symmetric probability density function; (2) mean μ, median, and

Normal Distribution

6.2: Standardisation

The process of converting a normal random variable X ~ N(μ, σ²) to a standard normal random variable Z ~ N(0, 1) using t

Normal Distribution

6.2: Standardisation

A standardized value representing how many standard deviations a value is from the mean. For X ~ N(μ, σ²), the z-score i

Normal Distribution

6.3: Normal Tables

Tables providing cumulative probabilities P(Z ≤ z) for the standard normal distribution, typically showing P(Z ≤ z) for

Normal Distribution

6.3: Normal Tables

The inverse normal process: given a probability p, find the z-score such that P(Z ≤ z) = p. This requires reverse lookup

Normal Distribution