A company performs quality control on its juice bottles. It finds that the volumes of juice in its 12 oz. bottles have a mean of 12.2 oz. and a standard deviation of 0.08 oz. Find the minimum and maximum "usual" values.

A. 12.12 oz., 12.28 oz.
B. 12.04 oz., 12.36 oz.
C. 11.96 oz., 12.44 oz.
D. 12.08 oz., 12.32 oz.

The minimum and maximum "usual" values for juice bottles, considering a normal distribution with a mean of 12.2 oz. and a standard deviation of 0.08 oz, are 11.96 oz. and 12.44 oz., respectively.

Explanation:

The company finds that its bottles of juice have a mean volume of 12.2 oz. and a standard deviation of 0.08 oz. To find the minimum and maximum "usual" values, we use the concept of a standard range, which typically extends three standard deviations from the mean in both directions in a normal distribution. Considering the rule of thumb that 99.7% of the data lies within three standard deviations of the mean in a normal distribution, we calculate:

The minimum "usual" value = mean - (3 × standard deviation) = 12.2 oz. - (3 × 0.08 oz.) = 12.2 oz. - 0.24 oz. = 11.96 oz.
The maximum "usual" value = mean + (3 × standard deviation) = 12.2 oz. + (3 × 0.08 oz.) = 12.2 oz. + 0.24 oz. = 12.44 oz.

Therefore, the minimum and maximum "usual" values for the juice bottles are 11.96 oz. and 12.44 oz., respectively. These values are the boundaries within which we expect most (99.7%) of the juice volumes to fall if the distribution is normal.