Netherlands HAVO 5 (eindexamenjaar) Mathematics D
Chapters: 2
1. Statistics and probability (part 2)
Probability distributions · Applying statistical methods · Profile-specific deepening
- Binomial Distribution – Repeat the same yes/no trial n times, independently, with the same chance of success p each time. The number of successes X follows the binomial distribution B(n, p): P(X = k) = ⁿCₖ pᵏ qⁿ⁻ᵏ with q = 1 − p. Its mean is np and its variance is npq.
- Hypothesis Testing – A hypothesis test checks a claim about a population using a sample. Start with the null hypothesis H₀ (no change, e.g. p = 0.5) and the alternative H₁ (what we suspect, e.g. p > 0.5). Choose a significance level such as 5%. Work out how likely the sample result (or more extreme) is if H₀ were true: the p-value. If the p-value is below the level, or the result falls in the critical region, reject H₀. Otherwise there is not enough evidence to reject it. Type I error = rejecting a true H₀; Type II error = not rejecting a false H₀.
2. Mathematics in technology
Mathematics in technology
- Mathematical Modelling: Using Maths to Describe the Real World – A mathematical model is an equation, graph or table that describes a real situation in a simple way. The modelling cycle: understand the real problem → choose variables and make assumptions → build a model (for example linear, quadratic or exponential) → solve and predict → check the answer against real data → improve the model or state its limits. No model is perfect; a good one is simple and close enough to be useful.