The signed-rank statistic can be represented as S+ = W1 + W2 +...+ Wn, where Wi = i if the sign of the xi - μ0 with ith largest absolute magnitude is positive (in which case i is included in S+) and Wi = 0 if this value is negative (i=1,2,...,n). Furthermore, when H0 is true, the Wi's are independent and P(W=i) = P(W=0) = .5.
The Wi's aren't identically distributed (e.g., possible values of W2 are 2 and 0), so our Central Limit Theorem for identically distributed and independent variables can't be employed here when n is large. But, a more general CLT can be employed to assert that when H0 is true and n > 20, S+ has approximately a normal distribution with the mean and variance obtained in (a). Employed this to propose a large-sample standardized signed-rank test statistic and then an appropriate rejection region with level α for each of three commonly encountered alternative hypotheses.