Final answer:
A modern quality control standard that allows for 3.4 defects per one million opportunities is called Six Sigma. Using the empirical rule for a normal distribution and a mean of 10 defects with a standard deviation of 3, we can expect 68% of the samples to fall between 7 and 13 defects, 95% between 4 and 16, and 99.7% between 1 and 19 defects.
Step-by-step explanation:
A modern quality control standard that allows for 3.4 defects per one million opportunities is called Six Sigma. The goal of Six Sigma is to improve the quality of process outputs by identifying and removing the causes of defects and minimizing variability in manufacturing and business processes.
When applying the 68-95-99.7 empirical rule to a sample of n = 100 cars, we assume a normal distribution for the number of defective cars, X. If 10 percent of the cars were generally defective, the mean (μ) in our sample would be 10. Based on the standard deviation (σ), which is 3 in this example, we can calculate the expected range of defective cars using the z-scores for different confidence levels. For one standard deviation from the mean (z = ±1), 68 percent of the defective cars will fall between seven and thirteen cars. For two standard deviations (z = ±2), 95 percent fall between four and sixteen cars. For three standard deviations (z = ±3), 99.7 percent encompass between one and nineteen cars.