Six Sigma Computation and Interpretations

To what probabilities do each of the following sigma levels correspond to, based on a standard normal curve: 3 sigma, 4sigma, 5 sigma, and 6 sigma? (Hint: Use the NORMSDIST function in Excel. Note that this function returns the standard normal cumulative distribution function. The distribution has a meanof 0 (zero) and a standard deviationof one. Check Figures: for three sigma, two-tailed probabilityequals 0.27%; for six sigma, the two-tailed probability level is 0.0000002%) To what level of defects per million do each of the two-tailed probabilities correspond to? What is the point of these calculations?

Six Sigma Interpretations

To what probabilities do each of the following sigma levels correspond to, based on a standard normal curve: 3 sigma, 4sigma, 5 sigma, and 6 sigma? (Hint: Use the NORMSDIST function in Excel. Note that this function returns the standard normal cumulative distribution function. The distribution has a mean of 0 (zero) and a standard deviation of one. Check Figures: for three sigma, two-tailed probability equals 0.27%; for six sigma, the two-tailed probability level is 0.0000002%) To what level of defects per million do each of the two-tailed probabilities correspond to? What is the point of these calculations?

Please show steps to the answer
Answer

We are considering standard normal distribution, i.e., a normal distribution with mean zero and standard deviation one. Theoretically for a standard normal distribution n sigma level probability means . That is the required probability is probability from - to -n plus probability from n to . (Note that for a normal distribution sigma means the standard deviation). The one-sigma level probability is the shaded region in the following figure

This probability can be easily calculated …

The procedure for finding three sigma, four sigma, five sigma and six sigma values with the basic theory behind, computational procedure and interpretation are provided.