5 Climbing ropes produced by a manufacturer have breaking strengths which are normally distributed with mean 160 kg and standard deviation 11.3 kg . A group of climbers have weights which are normally distributed with mean 66.3 kg and standard deviation 7.1 kg .

1. Find the probability that a rope chosen randomly will break under the combined weight of 2 climbers chosen randomly. Each climber carries, in a rucksack, equipment amounting to half his own weight.
2. Find the mean and variance of the combined weight of a climber and his rucksack.
3. Find the probability that the combined weight of a climber and his rucksack is greater than 87 kg .