Question

Sodas in a can are supposed to contain an average of 12 ounces. This particular brand has a standard deviation of 0.1 ounces, with an average of 12.1 ounces. If the can's contents follow a Normal distribution, what is the probability that the mean contents of a six pack are less than 12 ounces?

Answer 1

Answer:

The probability that the mean contents of a six pack are less than 12 ounces is 15.87%.

Step-by-step explanation:

Problems of normally distributed samples can be 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

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

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.

In this problem, we have that:

$\mu = 12.1, \sigma = 0.1$

This probability is the pvalue of the zscore of $X = 12$

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

$Z = \frac{12 - 12.1}{0.1}$

$Z = -1$

Z = 1 has a pvalue of .1587.

This means that the probability that the mean contents of a six pack are less than 12 ounces is 15.87%.