1 The number of cars passing a speed camera on a main road between 9.30 am and 11.30 am may be modelled by a Poisson distribution with a mean rate of 2.6 per minute.
- Write down the distribution of \(X\), the number of cars passing the speed camera during a 5-minute interval between 9.30 am and 11.30 am .
- Determine \(\mathrm { P } ( X = 20 )\).
- Determine \(\mathrm { P } ( 6 \leqslant X \leqslant 18 )\).
- Give two reasons why a Poisson distribution with mean 2.6 may not be a suitable model for the number of cars passing the speed camera during a 1 -minute interval between 8.00 am and 9.30 am on weekdays.
- When \(n\) cars pass the speed camera, the number of cars, \(Y\), that exceed 60 mph may be modelled by the distribution \(\mathrm { B } ( n , 0.2 )\).
Given that \(n = 20\), determine \(\mathrm { P } ( Y \geqslant 5 )\).
- Stating a necessary assumption, calculate the probability that, during a given 5-minute interval between 9.30 am and 11.30 am , exactly 20 cars pass the speed camera of which at least 5 are exceeding 60 mph .