CAIE S1 2021 November — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2021
SessionNovember
TopicNormal Distribution
TypeMixed calculations with boundaries

4 Raj wants to improve his fitness, so every day he goes for a run. The times, in minutes, of his runs have a normal distribution with mean 41.2 and standard deviation 3.6.
  1. Find the probability that on a randomly chosen day Raj runs for more than 43.2 minutes.
  2. Find an estimate for the number of days in a year ( 365 days) on which Raj runs for less than 43.2 minutes.
  3. On 95\% of days, Raj runs for more than \(t\) minutes. Find the value of \(t\).