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?

   Hint (b):

   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.

   Hint (c):

   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.

   Hint (d):

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