90% confidence interval for mining a block?
Bitcoin blocks are mined according to a Poisson process with a mean of 10 minutes (600 seconds) if you assume constant network hash rate. The difficulty of mining blocks gets adjusted every 2016 blocks to address this variability.
Interarrival times of a Poisson process are exponentially distributed.
The 95th quantile of an exponential distribution with a parameter of 1/600 is 1797.4
The 5th quantile of an exponential distribution with a parameter of 1/600 is 30.8.
90 percent of the time an observation from an exponential distribution will fall in the interval of (30.8,1797.4) seconds
The median time is 415.9 seconds.