In: Statistics and Probability
Suppose that a factory that produces shampoo has a machine that fills containers with c mL to 724 mL of shampoo.The machine is calibrated to fill bottles with at least the labeled amount (700 mL) 80% of the time. (a) Find the value of c. (b) The company that sells the product is worried that they are losing a significant profit by selling too many bottles that are filled too much (significantly overfilled). Suppose that the company begins to lose money for any bottle that has 712 mL or more. Find the probability that at least one fourth of a batch of 100 bottles is significantly overfilled. (c) What is the expected value of the number of overfilled bottles? (d) Do you think the company should be worried about their profit margins? Explain using previous answers or other probabilities.