CAIE S2 2011 June — Question 1

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2011
SessionJune
TopicLinear combinations of normal random variables
TypePure expectation and variance calculation

1 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 \(T \mathrm {~kg}\). Find the mean and standard deviation of \(T\).
\(2 X\) is a random variable having the distribution \(\mathrm { B } \left( 12 , \frac { 1 } { 4 } \right)\). A random sample of 60 values of \(X\) is taken. Find the probability that the sample mean is less than 2.8 .