CAIE S2 2019 June — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2019
SessionJune
TopicLinear combinations of normal random variables
TypeFixed container with random contents

4 A factory supplies boxes of children's bricks. Each box contains 10 randomly chosen large bricks and 20 randomly chosen small bricks. The masses, in grams, of large and small bricks have the distributions \(\mathrm { N } ( 60,1.2 )\) and \(\mathrm { N } ( 30,0.7 )\) respectively. The mass of an empty box is 8 g . Find the probability that the total weight of a box and its contents is less than 1200 g .