You are the statistician responsible for quality standards at a cheese factory.

You want the probability that a randomly chosen block of cheese labelled

"1 kg" is actually less than 1 kilogram (1000 grams) to be 1% or less. The weight (in grams) of blocks of cheese produced by the machine is normal

(a) Calculate your posterior probability distribution.

(b) Calculate your posterior probability that µ < 1000.

(c) Should you adjust the machine?