(1) The weight W of a person is 100 kg. Unforunately, the weighing machine is not accurate. Suppose the reading R is given by the expression R = W + E where E is the error in the machine and has normal distribution with mean 0 and std. dev. 2.

(a) what is the distribution of the reading given by the weighing machine?

(c) What is the probability that the reading is 2kg more than what the person actually weighs?