- A baker produces bread buns and bread rolls. The weights of buns, \(B\) grams, and the weights of rolls, \(R\) grams, are such that \(B \sim \mathrm {~N} \left( 55,1.3 ^ { 2 } \right)\) and \(R \sim \mathrm {~N} \left( 51,1.2 ^ { 2 } \right)\)
A bun and a roll are selected at random.
- Find the probability that the bun weighs less than \(110 \%\) of the weight of the roll.
Two buns are chosen at random.
- Find the probability that their weights differ by more than 1 gram.
The baker sells bread in bags. Each bag contains either 10 buns or 11 rolls. The weight of an empty bag, \(S\) grams, is such that \(S \sim \mathrm {~N} \left( 3,0.2 ^ { 2 } \right)\)
- Find the probability that a bag of buns weighs less than a bag of rolls.