Distribution of Sample Means. Assume that cans of Coke are filled so that the actual amounts have a mean of 12.00 ounces. A random sample of 36 cans has a mean amount of 12.19 ounces. The distribution of sample means of size 36 is normal with an assumed mean of 12.00 ounces, and those sample means have a standard deviation of 0.02 ounce.

a. How many standard deviations is the sample mean from the mean of the distribution of sample means?

b. In general, what is the probability that a random sample of size 36 has a mean of at least 12.19 ounces?

c. Does it appear that consumers are being cheated? Why or why not?