CAIE S2 2011 June — Question 5

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2011
SessionJune
TopicLinear combinations of normal random variables
TypeSame variable, two observations

5 Cans of drink are packed in boxes, each containing 4 cans. The weights of these cans are normally distributed with mean 510 g and standard deviation 14 g . The weights of the boxes, when empty, are independently normally distributed with mean 200 g and standard deviation 8 g .
  1. Find the probability that the total weight of a full box of cans is between 2200 g and 2300 g .
  2. Two cans of drink are chosen at random. Find the probability that they differ in weight by more than 20 g .