The manufacturer of the soft drink Crazy Caffeine Cola advertises that their bottles contain 500 ml of the product. For the purposes of quality control, the bottle filling process is periodically tested to ensure that the average volume per bottle does not differ significantly from 500ml. A random sample of 22 bottles yielded a mean volume of 495.6 ml. Assume that the population standard deviation is known to be 4.1 ml.

a) Compute and interpret a 99% confidence interval for the average volume of all cans. Should the manufacturer be concerned about this result?

b) In addition to the fact a random sample was taken, what other condition is needed for the result of part a to be valid?

c) Suppose the manufacturer wants their estimated mean to be within 1.1 ml of the true mean with 99% confidence. How many bottles should they sample?