4. Accidents occur randomly at a crossroads at a rate of 0.5 per month. A researcher records the number of accidents, \(X\), which occur at the crossroads in a year.
- Find \(\mathrm { P } ( 5 \leqslant X < 7 )\)
A new system is introduced at the crossroads. In the first 18 months, 4 accidents occur at the crossroads.
- Test, at the \(5 \%\) level of significance, whether or not there is reason to believe that the new system has led to a reduction in the mean number of accidents per month. State your hypotheses clearly.