Sorry, no. I don’t think you have a normal distribution with cycle time data. A non-parametric test should be used (You don’t say what the sample size was to collect the baseline for your average and sd, but with ). Typically you would use a discrete sample size calculation.
In probability theory and statistics, the Poisson distribution (pronounced [pwas??]) (or Poisson law of small numbers) is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and independently of the time since the last event. (The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.)