What is the Average Bitcoin Confirmation Time?
There is a greater than 60% chance your transaction will be confirmed within 10 minutes if you pay a high enough fee:
Minutes waited Probability of block being found
0 0%
10 62%
20 85%
30 96%
40 98%
50 99%
60+ 100%
I think it is not the case. Average waiting time for a block to be found is always 10 minutes. Be the last block mined 0 seconds ago or 10 minutes ago (Poisson distibution).
I don't know either where you got the above probabilities. We recently hadd a two hours gap between blocks. So it has proven wrong also on the last row.
There is no way for you to speed up the rate at which blocks are added to the blockchain. However, you can speed up the likelyhood your transaction is included in the next block by increasing the fees you pay for the transaction.
This is debatable, if you pay a fee that is higher of the lowest fee, increasing the fee has no effect. Once you buy the tickert for the next block, paying more than the minimum has no effect, you are actually wasting precious sats.
If your transaction stuck, there are a few ways to fix a stuck transaction. One way is to do a replace by fee (RBF) transaction. The other is to do a child-pays-for-parent (CPFP) transaction. You can also use a bitcoin accelerator service, but this is very expensive and not advisable anymore since there are other options. These are more advanced techniques, so we wrote up an entire page about all of them
here.
Of course you cannot use bothRBF and CPFP. It depends if you are the sender or the receiver of such transaction.