1 The number of insurance policy sales made per month by a salesperson is modelled by the random variable \(X\), with probability distribution shown in the table.
| \(r\) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| \(\mathrm { P } ( \mathrm { X } = \mathrm { r } )\) | 0.05 | 0.1 | 0.25 | 0.3 | 0.15 | 0.1 | 0.05 |
- Find each of the following.
- \(\mathrm { E } ( X )\)
- \(\operatorname { Var } ( X )\)
The salesperson is paid a basic salary of \(\pounds 1000\) per month plus \(\pounds 500\) for each policy that is sold. - Find the mean and standard deviation of the salesperson's monthly salary.