CAIE S2 2013 June — Question 3

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2013
SessionJune
TopicLinear combinations of normal random variables
TypeFixed container with random contents

3 Weights of cups have a normal distribution with mean 91 g and standard deviation 3.2 g . Weights of saucers have an independent normal distribution with mean 72 g and standard deviation 2.6 g . Cups and saucers are chosen at random to be packed in boxes, with 6 cups and 6 saucers in each box. Given that each empty box weighs 550 g , find the probability that the total weight of a box containing 6 cups and 6 saucers exceeds 1550 g .