Normal tail and interval probabilities, all of three independent items above a value and a value below which a given proportion lies

A machine fills bottles with lemonade. The volume of lemonade in a bottle is normally distributed with mean \(502\) ml and standard deviation \(3.5\) ml.

1. A bottle is chosen at random. Find the probability that it contains[5]
   1. more than \(506\) ml;
   2. at most \(497\) ml;
   3. between \(497\) ml and \(506\) ml.
2. Three bottles are chosen at random. Find the probability that each of the three bottles contains more than \(506\) ml.[2]
3. \(80\%\) of the bottles contain less than \(v\) ml. Find the value of \(v\), correct to one decimal place.[2]