You are the statistician responsible for quality standards at a cheese factory. You want the probability that a randomly chosen block of cheese labelled \(1 \mathrm{~kg}\) is actually less than 1 kilogram (1,000 grams) to be \(1 \%\) or less. The weight (in grams) of blocks of cheese produced by the machine is normal \(\left({ }^{2}\right.\) ) where \({ }^{2}=3^{2}\). The weights (in grams) of 20 blocks of cheese are:

You decide to use a discrete prior distribution for with the following probabilities:

(a) Calculate your posterior probability distribution.
(b) Calculate your posterior probability that \((c) Should you adjust the machine?

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