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While studying for exam I came across this practise problem which is giving me some trouble.

The amount , A, of wine in a bottle ~ N(1.05L, .0004L^{2}).

a)The bottle is labelled as containing 1L. What is the probability a bottle contains less than 1L?

b) Casks are available which have a volume, V, which is N(22L,.16L^{2}). What is the probability the contents of 20 randomly chosen bottles will fit inside a randomly chosen cask?

For (a), I simply did P(z < 1-1.05 / 0.02), and the correct answer being 0.0062.

However I am unsure how to approach (b). At first I thought i could just use the mean of the cask size (22L) and do P(Z<= 21-22 / 0.4), but it didnt work out.

Any help is appreciated thanks.

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# Normal Distribution problem

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