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. According to specifications, a soda-can filling machine must fill each can with a mean of $12$ ounces of soda and a standard deviation of $0.33$ ounces. The amount of soda in a can filled by filling machines can often be modeled with a normal distribution.

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 $= 1.5$.

   Answer (a):

   

2. How often do you actually get a $12$ oz can of soda containing more than $12$ oz?

   Hint (b):

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

3. What percent of cans contain between $11.5$ and $12.5$ ounces of soda? Shade your diagram from part (a) to represent these cans.

   Hint (c):

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