12.12.

(a) An electronic device has failure time 7 whose distribution is given by N(100, 4). Suppose that in recording 7 an error is made whose value may be represented as a random variable X, uniformly distributed over (-1, 1). If X and T are independent, obtain the pdf of S = X + T in terms of +, the cdf of the distribution N(0, 1).

(b) Evaluate P(100 S 101). [Hint: Use Simpson's rule to approximate the integral.]