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Question

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

Solution

VerifiedAnswered 12 months ago

Answered 12 months ago

Step 1

1 of 3Considering that, if a random variable $x$ is described by the normal distribution with the mean $\mu=16$ and standard deviation $\sigma=0.02$, the variable $z=\frac{x-\mu}{\sigma}$ has the standard normal distribution, the goal is to find the probability that a random variable $z$ is less than

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

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