| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2002 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | F-test and chi-squared for variance |
| Type | Find critical region for F-test |
| Difficulty | Standard +0.8 This is a straightforward inverse probability question requiring F-distribution tables or technology to find critical values. While S4 is a Further Maths module (inherently harder), the question itself is routine application of distribution tables with no conceptual complexity—just looking up two tail probabilities that sum to 0.90. The 3-mark allocation confirms it's a standard bookwork exercise, placing it slightly above average difficulty mainly due to the advanced module context. |
| Spec | 5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
The random variable $X$ has an $F$ distribution with 10 and 12 degrees of freedom. Find $a$ and $b$ such that $\text{P}(a < X < b) = 0.90$.
[3]
\hfill \mbox{\textit{Edexcel S4 2002 Q1 [3]}}