  ### Home > INT3 > Chapter 4 > Lesson 4.4.2 > Problem4-119

4-119.

Due to natural variability in manufacturing, a $12$-ounce can of soda does not usually hold exactly $12$ ounces of soda. The quality control department at a soda factory allows cans to hold a little more or a little less. Thus, the amount of soda in full cans can often be modeled with a normal distribution. Suppose that a soda-can filling machine at a factory fills cans with a mean of $12$ ounces of soda and a standard deviation of $0.33$ ounces.

1. Use your calculator to create a graph of a normal distribution using normalpdf. Sketch the graph. An appropriate value for the maximum of the relative frequency axis is Ymax $=1.5$.

2. How often does the model predict that a $12$-ounce can of soda will contain more than $12$ ounces?

The mean is the center (middle) of a normal distribution.

3. According to the model, what percentage of cans contain between $11.5$ and $12.5$ ounces of soda? Shade your graph from part (a) to represent these cans.

normalcdf($11.5$, $12.5$, mean, standard deviation)

4. In what percentile is a can with $13$ ounces of soda? Explain what that means in the context of this problem.

See the hint for part (c). What are your upper and lower bounds? Looking at your graph may help.