Moderate -0.8 This question tests understanding of symmetry in probability distributions, requiring students to recognize that P(X < 5) = P(X > 3) by symmetry about x = 4, then use P(3 < X < 5) = 2P(X < 5) - 1. It's a straightforward application of a single concept with minimal calculation, making it easier than average.
The graph of the probability density function of a random variable \(X\) is symmetrical about the line \(x = 4\).
Given that \(\text{P}(X < 5) = \frac{20}{39}\), find \(\text{P}(3 < X < 5)\). [2]
The graph of the probability density function of a random variable $X$ is symmetrical about the line $x = 4$.
Given that $\text{P}(X < 5) = \frac{20}{39}$, find $\text{P}(3 < X < 5)$. [2]
\hfill \mbox{\textit{CAIE S2 2021 Q3 [2]}}