OCR S2 2011 January — Question 2

Exam BoardOCR
ModuleS2 (Statistics 2)
Year2011
SessionJanuary
TopicCentral limit theorem
TypeFinding n from sample mean distribution

2 The random variable \(H\) has the distribution \(\mathrm { N } \left( \mu , 5 ^ { 2 } \right)\). The mean of a sample of \(n\) observations of \(H\) is denoted by \(\bar { H }\). It is given that \(\mathrm { P } ( \bar { H } > 53.28 ) = 0.0250\) and \(\mathrm { P } ( \bar { H } < 51.65 ) = 0.0968\), both correct to 4 decimal places. Find the values of \(\mu\) and \(n\).