An engineer takes a sample of 5 steel I beams from a batch, and measures the amount they sag under a standard load. The amounts in mm are: 5.19 4.72 4.81 4.87 4.88 It is known that the sag is normal (µ, σ2) where the standard deviation σ = .25 is known.

(a) Use a normal (5, .52) prior for µ. Find the posterior distribution.

(b) For a batch of I beams to be acceptable, the mean sag under the standard load must be less than 5.20. ( µ < 5.20). Set this up as a hypothesis test stating clearly the null and alternative hypotheses.

(c) Perform the test at the 5% level of significance.