CAIE S2 2008 June — Question 3

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2008
SessionJune
TopicLinear combinations of normal random variables
TypeComparison involving sums or multiples

3 The lengths of red pencils are normally distributed with mean 6.5 cm and standard deviation 0.23 cm .
  1. Two red pencils are chosen at random. Find the probability that their total length is greater than 12.5 cm . The lengths of black pencils are normally distributed with mean 11.3 cm and standard deviation 0.46 cm .
  2. Find the probability that the total length of 3 red pencils is more than 6.7 cm greater than the length of 1 black pencil.