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

30.85% probability of one can less than 12 oz

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 = (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 = (X - \mu)/(\sigma)`

`Z = (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