Adding normally distributed noise to simulated data

I have plot the data: overall_intensity = initial_intensity * exp(-time/f_lifetime), with time on the x axis and overall_intensity on the y axis. I have to choose a mean and standard deviation and use them to plot this again with the added random noise. I've created the function but am unsure what values to input as mean and standard deviation, and how to calculate the noise from that. Is there a specific rule to choosing these values? From research I think I use a zero mean? I tried to calculate the sd from the variance of the overall_intensity, but that value doesn't seem correct so I'm unsure.