Single-sided normal distribution

From Example A6.2 we know that after 100 steps of the countercurrent extraction, solute A is normally distributed about tube 90 with a standard deviation of 3. To determine the fraction of solute in tubes 85-99, we use the single-sided normal distribution in Appendix lA to determine the fraction of solute in tubes 0-84 and in tube 100. The fraction of solute A in tube 100 is determined by calculating the deviation z (see Chapter 4)... 

The t values also fit a normal distribution. Here, one is making an assumption that the true population mean and SD are known, and because the Cl is being made to include the true mean, the 0.5 probability that p is beyond the calculated limits a is spread over both ends of the distribution (both tails). Here a two-sided interval,/ = 0.5 t value, is used. The uses in which a single tail (above or below the mean) is considered, a one-sided t value (p = 0.025 is used (equivalent to the two-sidedp = 0.05). The object then is (1) to have a defined total population statistic and (2) to examine where and with what confidence a sample value fits into this population. Some points need to be made concerning confidence limits. 

When the concentration of impurity follows a normal distribution in samples, the frequency of failure rate can be calculated (Table 7.1). These values are taken from a single side of the normal Gaussian error distribution, which can be found in statistics books such as the one by Montgomery and Runger.i... 

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