Judging a track record

A portfolio management service (PMS) shows five years of returns with an annualised Sharpe ratio of 0.8. (a) Compute the $t$-statistic of its mean excess return under the iid approximation. (b) How many years would the same Sharpe ratio need to reach $t = 3$, the threshold Harvey, Liu and Zhu (2016) recommend for new claims? (c) Suppose 100 managers have true Sharpe ratio 0 and five-year track records. Approximately how many will show a sample Sharpe ratio of at least 0.8? What does this imply for choosing a PMS by its track record?