Central Limit Theorem
- What are you being asked about?
| Individual | Mean | Proportion | |
|---|---|---|---|
| Mean | μ | μ | p |
| Standard Deviation | σ | σ √n | √ p(1 − p) n |
| Conditions | • Normal |
• n ≥ 30 • Normal |
• np ≥ 10 • n(1 − p) ≥ 10 • Normal |
| z-score | z = x − μ σ | z = x̄ − μ σ √n | z = p̂ − p √ p(1 − p) n |
| Other Equations | N/A | N/A |
• p̂ =
x
n
• x = p̂ × n |
|
Key Phrases: Probability |
• Individual • Random ____ Chosen |
• Mean |
• Proportion • Percent • x of n |
- Does it say: “differs by”?
| No | Differs By Less | Differs By More | |||
|---|---|---|---|---|---|
| Individual | Mean | Proportion | |||
|
Calculator Functions |
Follow normalcdf Rules |
• Lower: μ − x • Upper: μ + x • Mean: μ • SD: σ |
• Lower: μ − x • Upper: μ + x • Mean: μ • SD: σ √n |
• Lower: p − % • Upper: p + % • Mean: p • SD: √ p(1 − p) n |
• 1 − “Differs by Less”
• 2 × normalcdf (one of the sides) |
| Diagram | N/A |
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