You have studied the salmon in the river Loppa, and are more interested in the weight variations than in the mean weight. The salmon weight follows a Normal distribution \(\phi_{(\mu, \sigma)}(x)\), so you study the variance by means of \(\tau\). Your investigations have concluded that \(\tau \sim \gamma_{(19.5,44)}(t)\).

(a) Write down the cumulative probability distribution of \(\tau\) by means of a \(\chi^{2}\) distribution.

(b) Find the probability that \(\tau>0.64\).

(c) Find a value \(\tau_{0}\) such that \(P\left(\tau>\tau_{0}ight)=95 \%\).

(d) Translate the results for \(\tau\) into results for \(\sigma\).