A civil engineer finds it appropriate to model the water level of a town's reservoir with a Normal distribution with mean 15 metres and standard deviation 2.5 metres. The reservoir has a wall 20 metres high and water will flow over and flood the town if the water level goes beyond 20 metres. If the water level drops below 10 metres, water rationing is enforced.

a) Comment briefly on the limitations of using a Normal distribution to model the water level.

b) Calculate the probability that the town is flooded given a current water level more than 17.5 metres.

c) Calculate the probability that the water rationing is enforced given a current water level less than 12.5 metres.

you may use R.