You have studied Oh Mega's production of capacitors. Just as with the resistors in Example 10.3.3, their values follow a Normal distribution \(\phi_{(\mu, \sigma)}(x)\), and just as in the case of the resistors, you study \(\tau\), and get that \(\tau \sim \gamma_{(16,4)}(t)\).

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

(b) Find the probability that \(\tau<6\).

(c) Find a value \(\tau_{0}\) such that \(P\left(\tau<\tau_{0}ight)=90 \%\).

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