Edexcel S3 Specimen — Question 2

Exam BoardEdexcel
ModuleS3 (Statistics 3)
SessionSpecimen
TopicLinear combinations of normal random variables
TypeComparing two journey times

2. Philip and James are racing car drivers. Philip's lap times, in seconds, are normally distributed with mean 90 and variance 9. James' lap times, in seconds, are normally distributed with mean 91 and variance 12. The lap times of Philip and James are independent. Before a race, they each take a qualifying lap.
  1. Find the probability that James' time for the qualifying lap is less than Philip's. The race is made up of 60 laps. Assuming that they both start from the same starting line and lap times are independent,
  2. find the probability that Philip beats James in the race by more than 2 minutes.