CAIE S2 2011 June — Question 1 4 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2011
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear combinations of normal random variables
TypePure expectation and variance calculation
DifficultyModerate -0.5 This is a straightforward application of the properties of sums of independent normal variables (mean and variance add). It requires only direct recall of formulas: μ_T = 3μ and σ_T = √3σ, with simple arithmetic. No problem-solving or conceptual insight needed, making it slightly easier than average.
Spec5.04a Linear combinations: E(aX+bY), Var(aX+bY)

The weights of bags of fuel have mean 3.2 kg and standard deviation 0.04 kg. The total weight of a random sample of three bags is denoted by \(T\) kg. Find the mean and standard deviation of \(T\). [4]

Question 1:
AnswerMarks
1E(T) = 9.6
Var(wt of one bag) = 0.0016
Var(T) = 3 × 0.0016
AnswerMarks
sd of T = √(3 × 0.0016) = 0.0693B1
M1
M1
AnswerMarks
A1 [4]May be impl. by Var(T) = 0.0048 or
0.0144
[Total: 4]
Question 1:
1 | E(T) = 9.6
Var(wt of one bag) = 0.0016
Var(T) = 3 × 0.0016
sd of T = √(3 × 0.0016) = 0.0693 | B1
M1
M1
A1 [4] | May be impl. by Var(T) = 0.0048 or
0.0144
[Total: 4]
The weights of bags of fuel have mean 3.2 kg and standard deviation 0.04 kg. The total weight of a random sample of three bags is denoted by $T$ kg. Find the mean and standard deviation of $T$. [4]

\hfill \mbox{\textit{CAIE S2 2011 Q1 [4]}}