Could you please use EXCEL (norm.inv among others) for example.Thanks

Question 4 (a) A Land Transport Authority engineer is carrying out a study on human and vehicle traffic at a major road junction during peak hour. Unknown to him, the traffic lights at the junction are programmed to change from green to red every 90 seconds. The engineer records the average time spent waiting for the lights to change by pedestrians who arrive at the junction randomly. He also observes that the mean arrival rate of vehicles at this junction is 5 cars in a 10 second time period. (1) Assuming that the waiting time at the traffic light is uniformly distributed, how long is a randomly selected pedestrian expected to wait before he/she can cross the road safely? (2 marks) (ii) Obtain the standard deviation of the pedestrian's waiting time. (2 marks) (iii) If the engineer were to sample 1000 pedestrians, what would be the average waiting time? (2 marks) (iv) If the engineer samples 20 pedestrians only, what is the probability that the average waiting time exceeds 50 seconds? (3 marks Compute the probability that 10 or more vehicles will arrive at the junction in a 10 second interval. (3 marks) (vi) How long does it take, on average, for the next car to arrive? (2 marks) (vii) Find the probability that no vehicle will stop at the traffic light for as long as 5 seconds. (2 marks) Question 4 (a) A Land Transport Authority engineer is carrying out a study on human and vehicle traffic at a major road junction during peak hour. Unknown to him, the traffic lights at the junction are programmed to change from green to red every 90 seconds. The engineer records the average time spent waiting for the lights to change by pedestrians who arrive at the junction randomly. He also observes that the mean arrival rate of vehicles at this junction is 5 cars in a 10 second time period. (1) Assuming that the waiting time at the traffic light is uniformly distributed, how long is a randomly selected pedestrian expected to wait before he/she can cross the road safely? (2 marks) (ii) Obtain the standard deviation of the pedestrian's waiting time. (2 marks) (iii) If the engineer were to sample 1000 pedestrians, what would be the average waiting time? (2 marks) (iv) If the engineer samples 20 pedestrians only, what is the probability that the average waiting time exceeds 50 seconds? (3 marks Compute the probability that 10 or more vehicles will arrive at the junction in a 10 second interval. (3 marks) (vi) How long does it take, on average, for the next car to arrive? (2 marks) (vii) Find the probability that no vehicle will stop at the traffic light for as long as 5 seconds. (2 marks)