Moderate -0.8 This is a straightforward application of variance rules for linear combinations of independent random variables. Students only need to recall that Var(aX + bY) = a²Var(X) + b²Var(Y) for independent variables, substitute the given standard deviations (converting to variances), and take the square root. It's a single-step calculation with no problem-solving or conceptual challenge beyond basic formula recall.
sd \(= 32.3\) or \(6\sqrt{29}\) or \(\sqrt{1044}\)
M1
A1
M1 for \(16\) (or \(4^2\)) & \(25\) (or \(5^2\)) used
M1 for add any multiples of \(9\) and \(36\) only
Answer
Marks
Total
3
Question 1:
Var $= 16 \times 9 + 25 \times 36$ ($= 1044$) | B1
sd $= 32.3$ or $6\sqrt{29}$ or $\sqrt{1044}$ | M1
| A1
M1 for $16$ (or $4^2$) & $25$ (or $5^2$) used
M1 for add any multiples of $9$ and $36$ only
Total | 3
1 The independent random variables $X$ and $Y$ have standard deviations 3 and 6 respectively. Calculate the standard deviation of $4 X - 5 Y$.
\hfill \mbox{\textit{CAIE S2 2015 Q1 [3]}}