5. The masses, \(X\), in kg, of men who work for a large company are normally distributed with mean 75 and standard deviation 10.
- Find the probability that the mean mass of a random sample of 5 men is less than 70 kg .
- The mean mass, in kg , of a random sample of \(n\) men drawn from this distribution is \(\bar { X }\). Given that \(\mathrm { P } ( \bar { X } > 80 )\) is approximately \(0 \cdot 007\), find \(n\).
The masses, in kg, of women who work for the company are normally distributed with mean 68 and standard deviation 6 . A lift in the company building will not move if the total mass in the lift is more than 500 kg .
- A random sample of 3 men and 4 women get in the lift. Find the probability that the lift will not move.
- State a modelling assumption you have made in calculating your answer for part (c).