Capacitors: You have measured the capacitance of FR Electronics's smallest capacitors. From a sample of 25 measurements, you got an average of \(\bar{c}=49.19 \mu \mathrm{F}\), and a sample standard deviation of \(s_{c}=2.15 \mu \mathrm{F}\). Assume the capacitance of this kind of capacitor follows a Normal distribution \(\phi_{(\mu, \sigma)}\) with unknown values for \(\mu\) and \(\sigma\). Use a neutral prior, and find the probability distributions of \(\mu\) and \(\tau\), and find the probability that a randomly selected capacitor of this kind has a capacitance of more than \(50 \mu \mathrm{F}\).