The Standard Normal Distribution with a mean of 0 and a standard deviation of 1

Question

The Standard Normal Distribution with a mean of 0 and a standard deviation of 1 has been used to calculate areas under the normal distribution curve. Quality control analysts were content to confine all data within +/- three standard deviations from the mean. The Ford Motor Company in the mid 1980s decided to try to confine all data within +/- four standard deviations from the mean. Six Sigma, the newest quality venture, is trying to confine all data within +/- six standard deviations from the mean. If the distance between the mean and the three, four, and six sigma limits is the same for all three, what must be happening to the value of the standard deviation and what impact might that have in the control of quality and the production of usable outputs?

The below is an answer i founf but i need a more clear explanation to the question being asked.

Answer:

within a sd

Xbar a *sd

if for a = 3,4 6

values are same, it means

sd tend to 0 .

it means there is very very small variation in the data points .

Explanation / Answer

If the distance between mean and three, four, six sigma limits is the same this means standard deviation is same and very litttle for three, four and six sigma limits.

This indicate that there is nigligable defective items in the production process and process is well in statistical control.

The distance between mean and three, four and six sigma limits is same means there is no impact of the specification limits on the production process.

Note that, for any production process the standard deviation may not be zero it is very small.

Mu + 3 * sigma

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