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 \(\mathrm{mm}\) are:

It is known that the sag is normal( \({ }^{2}\) ) where the standard deviation \(=25\) is known.
(a) Use a normal (5 \(\left.55^{2}\right)\) prior for . 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. ( \(
(c) Perform the test at the \(5 \%\) level of significance.

Transcribed Image Text:

5.19 4.72 4.81 4.87 4.88