Specialist2025 Exam 2 Section A · Q20CAS active1 mark

Linear combination of normal random variables

Let $P \sim \mathrm{N}\left(-2, 2^2\right)$ , $Q \sim \mathrm{N}\left(3, 3^2\right)$ , $R \sim \mathrm{N}\left(5, 6^2\right)$ and $Z \sim \mathrm{N}(0, 1)$ .

Given that $P$ , $Q$ and $R$ are independent random variables, $\Pr\left(3P + 2Q - R > 25\right)$ is equal to

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\Pr\left(Z > \frac{5\sqrt{3}}{3}\right)

\Pr(Z > 5)

\Pr\left(Z > \frac{5\sqrt{66}}{11}\right)

\Pr\left(Z > \frac{30}{7}\right)

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