Moderate -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.
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]
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]}}