You are following the band Pnk Flyd, and just attended a concert with a rather permeating smell

You are following the band Pünk Flöyd, and just attended a concert with a rather permeating smell of sweet smoke. The police had conducted random checks of 10 audience members, and had in total impounded 54.4 grams of hashish. The individual weights were as follows: 5.8, 6.0, 1.8, 3.4, \(6.8,4.7,7.8,6.1,6.0\), and 6.0 grams. Use a neutral prior, and find a \(90 \%\) credible interval for the mean possession in the audience. In addition, find a \(90 \%\) predictive interval estimate for the amount of hashish possessed by a random member of the audience \(\left(X_{+}ight)\), and credible intervals for \(\tau\) and \(\sigma\).