CAIE S1 2005 June — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2005
SessionJune
TopicNormal Distribution
TypeIndependent events across days/trials

6 Tyre pressures on a certain type of car independently follow a normal distribution with mean 1.9 bars and standard deviation 0.15 bars.
  1. Find the probability that all four tyres on a car of this type have pressures between 1.82 bars and 1.92 bars.
  2. Safety regulations state that the pressures must be between \(1.9 - b\) bars and \(1.9 + b\) bars. It is known that \(80 \%\) of tyres are within these safety limits. Find the safety limits.