The times, \(T\) minutes, taken by a random sample of 75 students to complete a test satisfy \(\sum t=230\) and \(\sum t^2=930\).

(a) Calculate unbiased estimates of the population mean and variance of T. [3]

Assume these estimates are the true population mean and variance. Another random sample of 75 students is taken and its mean is denoted by \(\overline T\).

(b) Find \(a\) such that \(P(\overline T>a)=0.234\). [3]