# Thread: Normal posterior distribution

1. ## Normal posterior distribution

Hi all!

The weights of items from a certain production processes are independently and
identically distributed, each with a N( $\theta$ , 4) distribution. The production manager believes that $\theta$ 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 $\theta$ .
Determine the predictive distribution for the weight of one further item from
the batch.

Any ideas on how to set out this problem?

Thanks!

2. This is from a bayesian statistics background btw