Question 993926
the z factor is equal to (x - m) / s


x is the raw score.
m is the mean.
s is the standard deviation.


the critical z factor is the z-score of the cutoff value.


if the bottle contains less than 15.86 ounces of drink, then it is rejected.


that makes the cutoff z factor equal to (15.86 - 16) / .32 = -.44


look up a z-score of -.44 in the z-score table and you will get .33


that means that 33% of the z-scores in the normal distribution table are below a z-score of .44.


that means that 33% of the bottles would be rejected if the amount of drink in the bottles was normally distributed with a mean of 16 ounces and the cutoff was any bottle that had less than 15.86 ounces of drink in it.


you can see the results in the following z-score calculator outputs.


the first output is based on the raw score.


the second output is based on the z-score.


the different in percentage is due to rounding of the z-score.


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