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In a bottle-filling process, the amount of drink injected into 16oz16 \mathrm{oz} bottles is normally distributed with a mean of 16oz16 \mathrm{oz} and a standard deviation of .02oz.02 \mathrm{oz}. Bottles containing less than 15.95oz15.95 \mathrm{oz} do not meet the bottler's quality standard. What percentage of filled bottles do not meet the standard?

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Answered 12 months ago
Answered 12 months ago
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Considering that, if a random variable xx is described by the normal distribution with the mean μ=16\mu=16 and standard deviation σ=0.02\sigma=0.02, the variable z=xμσz=\frac{x-\mu}{\sigma} has the standard normal distribution, the goal is to find the probability that a random variable zz is less than

15.59160.02=2.5.\frac{15.59-16}{0.02}=-2.5.

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