Six sigma is a popular concept that is built on confidence intervals. Basically,

Question

Six sigma is a popular concept that is built on confidence intervals. Basically, 6 sigma is a confidence interval with a point estimate (mean) that has plus/minus 3 standard deviations of the mean. Recall that for a normal distribution, this confidence interval should capture almost 100% of all data in the distribution.

For something like coming to work, on a normal day I might build in a cushion time of 5 minutes, so I'm operating at 1 sigma. If I have an important meeting, I'll probably build in 3 sigmas, making me on time 99.87% of the time. If I think I'll be fired if I am late, I'll probably be at six sigmas. Or just sleep in my office the night before!

Please post an example to show the application of six sigma in your life. As one example, let's say my commute time is an average of 45 minutes, with a 5 minute standard deviation. Let's further define a "fail" as arriving after 9:00. If I leave at 8:15, I will fail 50% of the time. By building in a 5 minute cushion, leaving at 8:10, I'm at 1 sigma and will be on time 84.1% of the time. If I leave at 8:05, that's 2 sigmas and I'm on time 97.7% of the time. If I really wanted, I could be at 6 sigmas and leave at 7:45 and I'd be on time 99.999% of the time.

Explanation / Answer

My daily life example : Catchin a train at 6:00 in the morning. My commute time from home to Railway station is normally distributed with mean 20 minutes and standard deviation 2 minutes. Define "fail" as reaching the railway station after 5:55 in the morning. So, If I leave at 5:35, I will fail 50% of the time. By building in a 2 minute cushion, leaving at 5:33, I'm at 1 sigma and will be on time 84.1% of the time. If I leave at 5:31, that's 2 sigmas and I'm on time 97.7% of the time. If I really wanted, I could be at 6 sigmas and leave at 5:29 and I'd be on time 99.999% of the time.

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