A factory manufactures 100 Ohm electrical resistors. Due to imperfections in the production, the resistors are not exactly 100 Ohms, but have to be treated as a random variable which we will call X. The probability density function for X is a normal density with a mean 100 and variance 4.

a) Find the probability that X is less than or equal to 105 Ohms.

b) Now let's consider a second factory which also produces 100 Ohm resistors. Again, due to imperfections in the production, the resistors are not exactly 100 Ohms, but have to be treated as a random variable which we will call Y. The probability density function for Y is uniform distribution on the interval from 97 to 103 Ohms. You have two resistors X and Y, one from each factory. Let Z= X+Y. Find the mean and variance of Z. It is safe to assume that X and Y are independent.