a manually operated stopwatch is used to clock times in a 100 m track race. if the true time of a runner is t, the watch will show time t+0.1+X, where X has a normal distribution with expected value 0 and variance 0.01.

(a) for a given t, what is the distribution of T?

(b) if the true time t is 15 seconds, what is P(T<=11.5)?

(c) what is the probability that T is within 0.05 seconds of the true time t?