1. A car manufacturer tests the first 1,000 cars coming off the
assembly line to see if their new anti-lock braking system works
correctly. Use the typical values for control limits. What percentage
would be an expected outcome in a sample mean that is within ±3
standard deviations of the distribution mean?
A sampling distribution serves as the theoretical basis for distinguishing between random and nonrandom values of a sampling statistic. Very simply, limits are selected within which most values of a sample statistic should fall if its variations are random. The limits are stated in terms of number of standard deviations from the distribution mean. Typical limits are ± 2 standard deviations or ± 3 standard deviations. Figure 10.5 illustrates these possible limits and the probability that a sample statistic would fall within those limits if only random variations are present. Conversely, if the value of a sample statistic falls outside those limits, there is only a small probability (1 − 99.74 = .0026 for ± 3 limits, and 1 − 95.44 = .0456 for ± 2 limits) that the value reflects randomness. Instead, such a value would suggest nonrandomness.
2. A manager is concerned about process variation as it
pertains to employees' use of time. Which loss in this
situation results from excessive process variation?
Variation occurs in all business processes. It can be due to variety or variability. For example, random variability is inherent in every process; it is always present. In addition, variation can occur as the result of deliberate management choices to offer customers variety.
There are four basic sources of variation:
1.The variety of goods or services being offered. The greater the variety of goods and services, the greater the variation in production or service requirements.
2.Structural variation in demand. These variations, which include trends and seasonal variations, are generally predictable. They are particularly important...