OCR MEI S3 2016 June — Question 1

Exam BoardOCR MEI
ModuleS3 (Statistics 3)
Year2016
SessionJune
TopicLinear combinations of normal random variables
TypeMultiple stage process probability

1 A game consists of 20 rounds. Each round is denoted as either a starter, middle or final round. The times taken for each round are independently and Normally distributed with the following parameters (given in seconds).
Type of roundMeanStandard deviation
Starter20015
Middle22025
Final25020
The game consists of 4 starter, 12 middle and 4 final rounds. Find the probability that
  1. the mean time per round for the 4 final rounds will exceed 260 seconds,
  2. all 20 rounds will be completed in a total time of 75 minutes or less,
  3. the 12 middle rounds will take at least 3.5 times as long in total as the 4 starter rounds,
  4. the mean time per round for the 12 middle rounds will be at least 25 seconds less than the mean time per round for the 4 final rounds.