A certain beverage company is suspected of underfilling its cans of soft drink. The company advertises that its cans contain, on average, 12 ounces of soda with standard deviation 0.35 ounce. For the...

1. A certain beverage company is suspected of underfilling its cans of soft drink.  The company advertises that its cans contain, on average, 12 ounces of soda with standard deviation 0.35 ounce.  For the questions that follow, suppose that the company is telling the truth.

(a)  Can you calculate the probability that a single randomly selected can contains 11.9 ounces or less?  If so, find the probability.  If not, explain why you cannot.

(b)  A quality control inspector measures the contents of a random sample of 100 cans of the company’s soda and calculates the sample mean .  What is the shape, mean and standard deviation of the sampling distribution of  for samples of size n = 100?

(c) The inspector in part (b) obtains a sample mean of 11.9 ounces.  Calculate the probability that a random sample of 100 cans produces a sample mean amount of 11.9 ounces or less. (you do
NOT
have to do the full State/Plan/Do/Conclude here)

(d) Given that the inspector found an average of 11.9 ounces in their sample, and the probability of that result that you found in part (c) (assuming the company is being truthful), would you conclude that the company is telling the truth about how much soda is in each can?  Justify your answer.