A manufacturer fills bottles with oil. The volume of oil in a bottle, $$\(V \mathrm{ml}\)$$, is normally distributed with $$\(V \sim \mathrm{N}\left(100,2.5^{2}\right)\)$$ (a) Find $$\(\mathrm{P}(V> 104.9)\)$$ (3) (b) In a pack of 150 bottles, find the expected number of bottles containing more than $$\(104.9 \mathrm{ml}\)$$ (2) (c) Find the value of $$\(v\)$$, to 2 decimal places, such that $$\(\mathrm{P}(V> v \mid V< 104.9)=0.2801\)$$ (6)

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