SPS SPS FM Statistics 2024 April — Question 5

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2024
SessionApril
TopicNormal Distribution
TypeStandard two probabilities given

5. The random variable \(H\) has the distribution \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\). It is given that \(\mathrm { P } ( H < 105.0 ) = 0.2420\) and \(\mathrm { P } ( H > 110.0 ) = 0.6915\). Find the values of \(\mu\) and \(\sigma\), giving your answers to a suitable degree of accuracy.