Let X1,..., Xn be i.i.d. normal with mean and variance 1. Let X n be the

Let X1,..., Xn be i.i.d. normal with mean θ and variance 1. Let X¯ n be the usual sample mean and let X˜ n be the sample median. Let pn be the probability that X¯ n is closer to θ than X˜ n is. Determine limn→∞ pn.