Managing for Quality and Performance Excellence 9th Edition by James Evans,William Lindsay

Exercise 26

Note: Data sets for many problems in this chapter are available in the Excel workbook C06Data.xlsx on the Student Companion Site. Click on the appropriate worksheet tab as noted in the problem (e.g., Prob. 6-1) to access the data. In addition, the spreadsheet templates illustrated in the chapter are also available to aid in solving many of these problems.
A warehouse manager at Dockhousing, Inc. maintains a large inventory of video games. The company's database states that the mean value of the games in inventory is $50, with a standard deviation of $5. The manager is concerned about pilfering the more expensive games by the warehouse employees. She picked a random sample of 100 games and found the mean value to be $48.50. Assuming a normal distribution, what is the probability that the sample mean would be $48.50 or less if all the inventory can actually be accounted for? What conclusions would you reach?