7. An examiner believes that once she has marked the first 20 papers the time it takes her to mark one paper for a particular exam follows a Normal distribution. Having already marked more than 20 papers for each of the \(P 1\), M1 and S1 modules set one summer, the mean and standard deviation, in seconds, of the time it takes her to mark a paper for each module are as shown in the table below.
| \cline { 2 - 3 }
\multicolumn{1}{c|}{} | Mean | Standard Deviation |
| P1 | 252 | 17 |
| M1 | 314 | 42 |
| S1 | 284 | 29 |
- Find the probability that the difference in the time it takes her to mark two randomly chosen \(P 1\) papers is less than 5 seconds.
(6 marks) - Find the probability that it takes her less than 10 hours to mark \(45 M 1\) and \(80 S 1\) papers.
\section*{END}