If you
really want to find out how
long this song actually takes to sing, just do the following calculations:
1. Time yourself in reading one verse for each of the 1.0 x 10^(n) {for n=3,6,9,12,15}. You should have a total of five time intervals for each verse.
e.g. 1) for 999,999,999,999,999 bottles, it takes 60 seconds to complete one verse.
for 999,999 bottles, it takes 30 seconds to complete one verse.
2. Multiply the corresponding time interval for each "n".
e.g. 2) from e.g. 1), 999,000,000,000,000 x 60 = t_15, and 999,000 x 30 = t_6.
(Notice you are excluding the "9's" after the 10^(n).)
3. Add all the time intervals for each corresponding "n" together. This will give you an approximate time only. This initial estimate gives a generous amount of time that may exceed that of the actual time it might take to finish the song. However, factors such as:
a) the time it takes to keep track of the bottles;
b) the time it takes to rest the vocal chords;
c) the time it takes to consume water to lubricate the throat;
d) the extended time for vocal chord deterioration..
..are considered to balance-out the initial estimate. Thus, the initial estimate might actually turn out to be the actual estimate (ignoring eating, sleeping, and washroom time).
..Also, do not forget to convert the time to years, months, days, hours, minutes, seconds if you want a better estimate to schedule your life activities.
Here is my own calculation:
a)I first calculated how long it takes to say each worded verse:
"...bottles of beer on the wall." = 3 seconds
"...bottles of beer." = 2 seconds
"...if one of the bottles should happen to fall." = 3 seconds
Since the first verse occurs twice, it must be counted twice.
b) Then I calculated how long it takes to say the number:
999,999,999,999,999 = 15 seconds
999,999,999,999 = 9 seconds
999,999,999 = 6 seconds
999,999 = 4 seconds
999 = 2 seconds
c) Then the subtotals:
verse for 999,999,999,999,999 = 55 seconds
verse for 999,999,999,999 = 37 seconds
verse for 999,999,999 = 28 seconds
verse for 999,999 = 22 seconds
verse for 999 = 16 seconds
d) Then more subtotals:
999,000,000,000,000 x 55 seconds = 54945000000000000 seconds
999,000,000,000 x 37 seconds = 36963000000000 seconds
999,000,000 x 28 seconds = 27972000000 seconds
999,000 x 22 seconds = 21978000 seconds
999 x 16 seconds = 15984 seconds
e) The total is: 54981990993993984 seconds.
f) The conversion: 1738703924 years, 10 months, 15 days, 13 hours, 26 minutes, 24 seconds. (Using an average of 30.5 days per month.)
Therefore, the song does end but not in your lifetime, unless somehow, you become immortal.
I leave the standard deviation calculations up to someone else.