# Statistical Sciences 2035 Lecture Notes - Interval Estimation, Standard Deviation, Statistical Process Control

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1 Dec 2011
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## Document Summary

If the population distribution is bell-shaped (normal distribution), symmetrical with a single peak, with mean and standard deviation , then. 68. 26% of all population units are within (plus or minus) one standard deviation of the mean and thus lie in the interval [ , + ] 95. 44% of all population units are within (plus or minus) two standard deviations of the mean and thus lie in the interval [ 2 , + 2 ] 99. 73% of all population units are within (plus or minus) three standard deviations of the mean and thus lie in the interval [ 3 , + 3 ] An interval that contains a specified percentage of the individual measurements in a population is called a tolerance interval. Often we interpret the three-sigma interval [ 3 ] to be a tolerance interval that contains almost all of the measurements in a normally distributed population.