products. What are the chances that the factory will pass the QC inspection? 4.113 Credit/debit card market shares. The following table reports the worldwide credit card industry’s market share data. A random sample of 100 credit card users is to be questioned regarding their satisfaction with their card company. For simplification, assume that each card user carries just one card and that the market share percentages are the percentages of all worldwide card customers that carry each brand. Credit Card Market Share % Visa 50 Mastercard 26 American Express 2.5 UnionPay 20 JCB 1 Discover 0.5 Source: Based on Nilson Report data, January 2020.

a. Propose a procedure for randomly selecting the 100 card users.

b. For random samples of 100 card users, what is the expected number of customers who carry Visa? Discover?

c. What is the approximate probability that half or more of the sample of card users carry Visa? Mastercard?

d. Justify the use of the normal approximation to the binomial in answering the question in part

c. Applying the Concepts—Advanced 4.114 Industrial filling process. The characteristics of an industrial filling process in which an expensive liquid is injected into a container were investigated in the Journal of Quality Technology. The quantity injected per container is approximately normally distributed with mean 10 units and standard deviation .2 units. Each unit of fill costs $20 per unit. If a container contains less than 10 units (i.e., is underfilled), it must be reprocessed at a cost of $10. A properly filled container sells for $230.

a. Find the probability that a container is underfilled. Not underfilled.

b. A container is initially underfilled and must be reprocessed. Upon refilling, it contains10.60 units. How much profit will the company make on this container?

c. The operations manager adjusts the mean of the filling process upward to