You have studied the brightness of a certain type of star, and are interested in the variation. The brightness follows a Normal distribution \(\phi_{(\mu, \sigma)}(x)\), so you study the variance by means of \(\tau\). Your investigations have concluded that \(\tau \sim \gamma_{(101.5,15)}(t)\).

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

(b) Find the probability that \(\sigma>2\).

(c) Find a value \(\sigma_{0}\) such that \(P\left(\sigma<\sigma_{0}ight)=98 \%\).