3 At a launderette the process of cleaning a load of clothes consists of three stages: washing, drying and folding. The times in minutes for each process are modelled by independent Normal distributions with means and standard deviations as shown in the table.
| \cline { 2 - 3 }
\multicolumn{1}{c|}{} | Mean | Standard deviation |
| Washing | 35 | 2.4 |
| Drying | 46 | 3.1 |
| Folding | 12 | 2.2 |
- Find the probability that drying a randomly chosen load of clothes takes more than 50 minutes.
- It is given that for \(99 \%\) of loads of clothes the washing time is less than \(k\) minutes.
Find the value of \(k\).
- Determine the probability that the drying time for a randomly chosen load of clothes is less than the total of the washing and folding times.
- Determine the probability that the mean time for cleaning 5 randomly chosen loads of clothes is less than 90 minutes. You should assume that the time for cleaning any load is independent of the time for cleaning any other load.