CAIE S1 2010 June — Question 3

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2010
SessionJune
TopicNormal Distribution
TypeStandard two probabilities given

3 The random variable \(X\) is the length of time in minutes that Jannon takes to mend a bicycle puncture. \(X\) has a normal distribution with mean \(\mu\) and variance \(\sigma ^ { 2 }\). It is given that \(\mathrm { P } ( X > 30.0 ) = 0.1480\) and \(\mathrm { P } ( X > 20.9 ) = 0.6228\). Find \(\mu\) and \(\sigma\).