CAIE S2 2013 June — Question 5

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2013
SessionJune
TopicLinear combinations of normal random variables
TypeAll components random including container

5 Packets of cereal are packed in boxes, each containing 6 packets. The masses of the packets are normally distributed with mean 510 g and standard deviation 12 g . The masses of the empty boxes are normally distributed with mean 70 g and standard deviation 4 g .
  1. Find the probability that the total mass of a full box containing 6 packets is between 3050 g and 3150 g .
  2. A packet and an empty box are chosen at random. Find the probability that the mass of the packet is at least 8 times the mass of the empty box.