The mass, in kilograms, of a block of cheese sold in a supermarket is denoted by the random variable \(M\). The masses of a random sample of 40 blocks are summarised as follows. \[n=40,\qquad\sum m=20.50,\qquad\sum m^2=10.7280.\]

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

(b) The price, \$\(P\), of a block of cheese of mass \(M\) kg is found using the formula \(P=11M+0.50\).

(b) Find estimates of the population mean and variance of \(P\). [3]