I am looking for dx where exp(-((x+dx)/(2sigma))^2) - exp( -(x/2sigma)^2)
Assuming dx << x, this is approximated by a differential, (-xdx/sigma^2) * exp( -(x/2sigma)^2, or the relative drop of dx/sigma^2. You want it to be 1⁄2 (lost one person out of two), your x = 4 sigma, so dx=1/8 sigma, which is under a year. Of course, it’s rather optimistic to apply the normal distribution to this problem, to begin with.
Assuming dx << x, this is approximated by a differential, (-xdx/sigma^2) * exp( -(x/2sigma)^2, or the relative drop of dx/sigma^2. You want it to be 1⁄2 (lost one person out of two), your x = 4 sigma, so dx=1/8 sigma, which is under a year. Of course, it’s rather optimistic to apply the normal distribution to this problem, to begin with.