Normal distribution properties
Objective. Interpret parameters, symmetry and density.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
The normal distribution is a continuous probability distribution described by two parameters, the mean μ and standard deviation σ, producing a symmetric bell-shaped curve centred on μ. The total area under the curve equals 1, the curve is symmetric about x = μ, and roughly 68% of data lies within one standard deviation of the mean. For N(50, 16), the mean is 50 and the variance is 16, so σ = 4. Always distinguish between the variance (σ²) stated in notation and the standard deviation (σ) itself.
Worked example
State the mean and standard deviation of the normal distribution N(72, 25), a question on normal distribution properties.
- 1Identify the first parameter as the mean: μ = 72
- 2Identify the second parameter as the variance: σ² = 25
- 3Take the square root to find the standard deviation: σ = √25
- 4State σ = 5
Answer: Mean = 72, standard deviation = 5
Concept mastery
Based on your past attempts at this lesson — the question types to practise again come first.
Complete a practice set to see your concept breakdown here.
Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. A common mistake is treating the second parameter in N(μ, σ²) as the standard deviation directly instead of the variance, forgetting to take a square root. Always check whether the question gives σ or σ², and convert using σ = √(σ²) when needed.
Your progress
Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.
0 of 5 steps complete
Your place saves automatically as you read.