Normal distribution practice

Practice session

What you practise

Level 1: the percentage between μ − σ and μ + σ, between μ − 2σ and μ + 2σ, or from μ to a bound. Level 2: the percentage above or below a bound, and between any two rule-of-thumb bounds. Level 3: the lower or upper bound of the 68% or 95% region. Level 4: σ worked back from a percentage, mixed with the rest. The explanation and a calculator are on the normal distribution calculator page. Numbers use a decimal comma (97,5), as in Dutch schools.

Example

The travel time of a bus ride is normally distributed with μ = 60 minutes and σ = 5 minutes. Using the rules of thumb, what percentage is under 70 minutes?

1. (70 − 60) ÷ 5 = 2, so 70 = μ + 2σ
2. Left of μ lies 50%; between μ and μ + 2σ lies 34 + 13,5
3. 50 + 34 + 13,5 = 97,5%

Answer: 97,5%.

What you need to know

What the 2027 exam syllabus says about the normal distribution, as far as this module practices it.

havo · wiskunde A · domain E, subdomain E3

Using the three rules of thumb for an (approximately) normal distribution · source syllabus wiskunde A havo 2027 (Examenblad)

• Know the three rules of thumb: 68%, 95% and almost 100%
• Write a bound as μ + σ, μ − 2σ and so on
• Get percentages and bounds from the rules of thumb, and work back to σ

vwo · wiskunde A

Statistics and probability (domain E) belong to the school exam. In the list of concepts for the central exam, the normal distribution and the three rules of thumb are only ticked for havo wiskunde A · source syllabus wiskunde A vwo 2027 (Examenblad)

Formula sheet

Print-friendly: use Print in your browser.

• About 68% $$\mu -\sigma \le x\le \mu +\sigma$$
• About 95% $$\mu -2\sigma \le x\le \mu +2\sigma$$
• Almost 100% $$\mu -3\sigma \le x\le \mu +3\sigma$$

Standard deviation σ (standaardafwijking)

A measure of how far the observations lie from the mean μ on average: the larger σ, the wider the bell.

Practice with real exam questions on Examenblad.nl (in Dutch). We do not host past exams.

Frequently asked questions

Can I type the percent sign?

Yes. 97,5 and 97,5% are both marked correct.

Why do the questions use the rules of thumb and not exact values?

The questions say “Use the rules of thumb”. The answer is then a number that follows from 68%, 95% and almost 100%, such as 34, 16 or 2,5. The normal distribution calculator also shows the exact value.