OCR S3 2015 June — Question 1

Exam BoardOCR
ModuleS3 (Statistics 3)
Year2015
SessionJune
TopicLinear combinations of normal random variables
TypeAll components random including container

1 A laminate consists of 4 layers of material \(C\) and 3 layers of material \(D\). The thickness of a layer of material \(C\) has a normal distribution with mean 1 mm and standard deviation 0.1 mm , and the thickness of a layer of material \(D\) has a normal distribution with mean 8 mm and standard deviation 0.2 mm . The layers are independent of one another.
  1. Find the mean and variance of the total thickness of the laminate.
  2. What total thickness is exceeded by \(1 \%\) of the laminates?