90% confidence interval for mining a block? I did some math and found that the 90% confidence interval for bitcoin blocks is that the block will take less than 1381.6 seconds. I used the calculation ln(10)*600 with 10 being used because a 90% confidence interval means one in ten blocks are expected to fall outside of this range. Could this be considered a 90% confidence interval?
Note: this could change if the difficulty is expected to rise or drop. If block time is 576 seconds, for example, it becomes a 91% confidence interval. In practice this changes a lot once the difficulty adjustment has passed.
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.