Wow ! I didn't know the numbers when I read the question,
but with that much riding on it, I had to go look them up and
learn something. You probably could have done the same thing
and saved yourself some money, but it's too late for that. It's all
mine now, as soon as I finish writing this answer.
In the normal distribution, 68.27% of the values lie within one
standard deviation of the mean, 95.45% lie within two standard
deviations, and 99.73% lie with three standard deviations.
Within one sigma: 68.27% of 20,000 = 13,654
13,654 light bulbs will last between 190 days and 270 days.
Within two sigma: 95.34% of 20,000 = 19,068
19,068 light bulbs will last between 150 days and 310 days.
Here's the one you asked for:
Within three sigma: 99.73% of 20,000 = 19,946
19,946 light bulbs will last between 110 days and 350 days.
Only 54 light bulbs will burn out in less than 110 days
OR keep going more than 350 days.
OK. Now you owe me.
