Normal posterior distribution

Hi all!

The weights of items from a certain production processes are independently and

identically distributed, each with a N($\displaystyle \theta$ , 4) distribution. The production manager believes that $\displaystyle \theta$ varies from batch to batch according to a N(110, 0.4) distribution.

A sample of 5 items is randomly selected from a batch, giving data: 108, 109,

107.4, 109.6, 112. Derive the posterior distribution for $\displaystyle \theta$ .

Determine the predictive distribution for the weight of one further item from

the batch.

Any ideas on how to set out this problem?

Thanks!