Problem 1 : Fracly oil is sold in 900 milliliter (ml) cans. The mean volume of juice placed in a can is 880 ml with a standard deviation of 7.

Problem 1: Fracly oil is sold in 900 milliliter (ml) cans. The mean volume of juice placed in a can is 880 ml with a standard deviation of 7.8 ml. Assuming a normal distribution, what is the probability that the filling machine will cause an overflow in a can, that is, the probability that more than 900 ml will be placed in the can?

Problem 2: A new product is being tested by Zed Electronics to determine if it will continue to operate in a stable fashion under a variety of conditions. A sample of 400 were tested, and 60 failed the test. Determine a 90 percent confidence interval for the population proportion.

Problem 3: You are asked by the owner of the Moonbow Motel to develop a customer satisfaction survey to determine the percentage of customers who are dissatisfied with service. In the past year, 10,000 customers were serviced. She desires a 95 percent level of confidence with an allowable statistical error of ± 0.01. From past estimates, the manager believes that about 3.5 percent of customers have expressed dissatisfaction. What sample size should you use for this survey?

Problem 4: An electronic component at Ampcomp has a specification of 100 ± 0.4 ohms. Scrapping the component results in a $81 loss.

​a. What is the value of k in the Taguchi loss function?

​b. If the process at Ampcomp averages 99.75 ohms with a standard deviation of 0.2 ohms, what is the expected loss per unit?

Problem 5: Broadtred, Inc. makes automobile tires that have a mean life of 50,000 miles with a standard deviation of 2,500 miles. Using Excel functions (see Chapter 6), determine the following:

​a.What fraction of tires is expected to survive beyond 54,000 miles? 

​b.What fraction will survive fewer than 56,000 miles?

​​c.What length of warranty is needed so that no more than 2 percent of the tires will be expected to fail during the warranty period?