7 A queue of cars has built up at a set of traffic lights which are at red. When the lights turn green, the time for the first car to start to move has a normal distribution with mean 2.2 s and standard deviation 0.75 s . This time is the reaction time for the first car. For each subsequent car the reaction time is the time taken for it to start to move after the car in front starts to move. These reaction times have identical normal distributions with mean 1.8 s and standard deviation 0.70 s . It may be assumed that all reaction times are independent.

1. Calculate the probability that the reaction time for the second car in the queue is less than half of the reaction time for the first car.
2. Calculate the probability that the fifth car in the queue starts to move less than 10 seconds after the lights turn green.
3. State where, in part (i), independence is required.