Don and MJ,
Sounds like were looking for a two tailed t-test to determine the probability of an event occuring given the event, the known mean, and a known s.d. Two tails because you have chances to be on either side of the mean, even though you are only testing for one specific event.

If that is true (wait for Don to confirm this), then there are tables (published in statistics books) which will allow you to get that information OR your MS Excel spreadsheet should have a t-test function on it as well.

A t-test basically takes the event and determines how many S.d. from the mean it occured. The resulting factor of "how many standard deviations from the mean" (I think you quoted 1.5 above) can then be translated into the "probability of likelihood" of said event occuring given the mean and s.d. you have calculated through the tables or function in Excel.

Hope this helps. And I really hope Don, Cac, Zen and the other statistical experts agree with my thoughts too! :-)