OCR Further Statistics 2017 Specimen — Question 2

Exam BoardOCR
ModuleFurther Statistics (Further Statistics)
Year2017
SessionSpecimen
TopicLinear combinations of normal random variables
TypeMixed sum threshold probability

2 The mass \(J \mathrm {~kg}\) of a bag of randomly chosen Jersey potatoes is a normally distributed random variable with mean 1.00 and standard deviation 0.06. The mass Kkg of a bag of randomly chosen King Edward potatoes is an independent normally distributed random variable with mean 0.80 and standard deviation 0.04.
  1. Find the probability that the total mass of 6 bags of Jersey potatoes and 8 bags of King Edward potatoes is greater than 12.70 kg .
  2. Find the probability that the mass of one bag of King Edward potatoes is more than \(75 \%\) of the mass of one bag of Jersey potatoes.