Edexcel S3 — Question 3

Exam BoardEdexcel
ModuleS3 (Statistics 3)
TopicLinear combinations of normal random variables
TypeTwo or more different variables

3. The time that a school pupil spends on French homework each week is normally distributed with a mean of 55 minutes and a standard deviation of 10 minutes. The time that this pupil spends on English homework each week is normally distributed with a mean of 1 hour 30 minutes and a standard deviation of 18 minutes. Find the probability that in a randomly chosen week
  1. the pupil spends more than 2 hours in total doing French and English homework,
  2. the pupil spends more than twice as long doing English homework as he spends doing French homework.
    (6 marks)