5. The workers in a large office block use a lift that can carry a maximum load of 1090 kg . The weights of the male workers are normally distributed with mean 78.5 kg and standard deviation 12.6 kg . The weights of the female workers are normally distributed with mean 62.0 kg and standard deviation 9.8 kg . Random samples of 7 males and 8 females can enter the lift.

1. Find the mean and variance of the total weight of the 15 people that enter the lift.
2. Comment on any relationship you have assumed in part (a) between the two samples.
3. Find the probability that the maximum load of the lift will be exceeded by the total weight of the 15 people.
   (4)