SOLUTION: An important quality characteristic for softdrink bottlers is the amount of softdrink injected into each bottle. In a particular filling process, the number of ounces injected into

Question 1193056: An important quality characteristic for softdrink bottlers is the amount of softdrink injected into each bottle. In a particular filling process, the number of ounces injected into an 8-ounce bottle is approximately normally distributed with a mean of 8.00 ounces and a standard deviation of 0.05 ounce. Bottles that contain less than 7.90 ounces do not meet the bottler's quality standard. If 20,000 bottles are filled, approximately how many will meet the quality standard?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mean is 8 ounces.
standard deviation is .05 ounces.
z-score = (x - m) / s
x is the raw score
m is the raw mean
s is the standards deviation
z-score for a bottle hat contains less than 7.9 ounces is z = (7.9 - 8) / .05 = -2.
area to the left of that z-score is equal to .02275.
that means that 2.275% of the scores under the normal distribution curve are less than a z-score of -2.
that means that 2.275% of the bottles that are filled will have less than 7.9 ounces in them.
that means that 20,000 * .02275 = 455 bottles will not meet the quality standard, which means that 20,000 minus 455 = 19,545 will meet the quality standards.
your solution is that 19,545 bottles will meet the quality standards.

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