OCR S3 2014 June — Question 4

Exam BoardOCR
ModuleS3 (Statistics 3)
Year2014
SessionJune
TopicLinear combinations of normal random variables
TypeComparison involving sums or multiples

4 Cola is sold in bottles and cans. The volume of cola in a bottle is normally distributed with mean 500 ml and standard deviation 10 ml . The volume of cola in a can is normally distributed with mean 330 ml and standard deviation 8 ml . Find the probability that the total volume of cola in 2 randomly selected bottles is greater than 3 times the volume of cola in a randomly selected can.