Sampling distributions & Central Limit Theorem β infinite population, real people
β Population
The Building (N = β)
ΞΌ = β kg | Ο = β kg
The population distribution of weight X β infinite residents described by a known shape.
In practice ΞΌ and Ο are unknown.
β‘ Sample
The Elevator
n = β | x̅ = β kg | s = β kg
π ELEVATOR Β· n = 30
Total loadβ kg / max 2 500 kg
Sample mean xΜβkg
We only know this one sampleβ¦
We use xΜ to estimate the unknown population mean ΞΌ.
β’ Sampling Distribution of x̅
Distribution of x̅
μ̅ = β | σ̅ = σ/√n = β
Each bar is built from many elevator rides. The histogram of x̅ is close to a
Normal distribution β especially when n is large or the population is not too skewed.