Hi, would appreciate if anyone can answer this question. Thanks in advance.

Suppose you are consulting for a manufacturer of tea bags. Each bag is supposed to contain
5.5 grams of tea, and the lling process is known to have a standard deviation of 0.106 grams
per bag (assume a normal distribution). Of interest is whether there is a drift (change) in
the mean amount of tea per bag.
(a) Determine a prior distribution that has a mean matching the process speci cation and
contains the information of about one hundred observations.
(b) A sample of 40 bags nds an average of 5.494 grams per bag.
i. What is the posterior probability that the process is within 0.001 grams of its spec-
i cation? (Be sure to keep enough decimal places in your computations.)
ii. What is the posterior predictive probability that a new tea bag will contain at least
the labeled amount of 5.5 grams of tea?