Let X and Y be independent normally distributed random variables, with X having a mean of 0 and variance of 1, and Y having a mean of 1. The probability that X is greater than Y is 1/3. To find the standard deviation of Y, we first determine that the joint distribution of X-Y has a mean of -1 and variance equal to the sum of the variances of X and Y. Setting the probability that X-Y is greater than its mean equal to 1/3 allows us to solve for the standard deviation of Y as 2.06.