3 The times, \(T\) minutes, taken by a random sample of 75 students to complete a test were noted. The results were summarised by \(\Sigma t = 230\) and \(\Sigma t ^ { 2 } = 930\).
- Calculate unbiased estimates of the population mean and variance of \(T\).
You should now assume that your estimates from part (a) are the true values of the population mean and variance of \(T\). - The times taken by another random sample of 75 students were noted, and the sample mean, \(\bar { T }\), was found.
Find the value of \(a\) such that \(P ( \bar { T } > a ) = 0.234\).