A recent Gallup Poll dealt with the proportion of Canadians who favoured the various Prime Ministers. It found that only Pierre Trudeau did quite well, of all Prime Ministers in recent memory, and that the proportion favouring Brian Mulroney is quite low. A newspaper article included the following statement: "Results are based on 1,037 interviews with Canadian adults conducted July 6 - 9, 2006. Gallup says a sample this size is accurate within 4 percentage points, 19 in 20 times". In fact, the precision of their estimate of the population proportion was not 4 percentage points. Find the closest precision below, when estimating the population proportion at 50%.
a) .02
b) .025
c) .030
d) .035