Question

A soda filling machine is supposed to fill cans of soda with 12 fluid ounces. Suppose that the fills are actually normally distributed with a mean of 12.1 oz and a standard deviation of 0.2 oz. a) What is the probability of one can less than 12 oz

Answer 1

Answer:

30.85% probability of one can less than 12 oz

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 12.1, \sigma = 0.2$

a) What is the probability of one can less than 12 oz

This is the pvalue of Z when X = 12. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{12 - 12.1}{0.2}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3085

30.85% probability of one can less than 12 oz