give you 300 dollars if u get this right. you have my word The lifetimes of 20,000 light bulbs are normally distributed. The mean lifetime is 230 days. The standard deviation is 40 days. Find the values defined by the standard deviation in a normal distribution for 3 standard deviations.
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.
