The daily production of employees at a certain company varies depending on their length of service. The daily production of an employee with $n$ months of service ( $1 \leqq n \leqq 100$ ) follows a normal distribution with mean $a n + 100$ ( $a$ is a constant) and standard deviation 12. When the probability that the daily production of an employee with 16 months of service is 84 or less is 0.0228, find the probability that the daily production of an employee with 36 months of service is at least 100 and at most 142 using the standard normal distribution table.
| $z$ | $\mathrm { P } ( 0 \leqq Z \leqq z )$ |
| 1.0 | 0.3413 |
| 1.5 | 0.4332 |
| 2.0 | 0.4772 |
| 2.5 | 0.4938 |
[3 points]
(1) 0.7745
(2) 0.8185
(3) 0.9104
(4) 0.9270
(5) 0.9710