Question

Lucullus Company sells specialty chocolate in packages marked 525 grams. In reality, Lucullus has set the process mean at -8 grams off the marked weight, and the process currently has a standard deviation of 21 grams. Suppose the customer will accept anywhere between +/- 42 from the marked weight as long as the average package has approximately 525 grams. As everyone likes chocolate, the buyers of Lucullus chocolate specify that 99.7% of the total packages should comply with the weight criteria, but they don't really mind that the packages contain more than expected amount of chocolate. However, the customers would really be dismayed if the chocolate packages show a weight that is below the lower tolerance limit. Do the current processes of Lucullus have the capability to conform to the weight and tolerance requirements?

Answer 1

The current processes of Lucullus Company should meet the weight and tolerance requirements set by customers as the process mean and standard deviation indicate that the chocolate packages will generally weigh more than the lower tolerance limit and fewer than 0.3% would potentially fail to meet this standard.

Step-by-step explanation:

To assess if the current processes of Lucullus Company conform to the weight and tolerance requirements, we need to consider the specifications given and the statistical properties of the process. The chocolate packages are marked at 525 grams; however, with a process mean set at 8 grams below the marked weight, this implies the actual mean weight of the chocolates is 517 grams. Considering the acceptable weight range is between 483 grams (525 - 42) and 567 grams (525 + 42), the mean process weight is above the lower limit, which is good since customers are mainly concerned with underweight packages.

The process has a standard deviation of 21 grams. According to the Empirical Rule, also known as the 68-95-99.7 rule, for a normally distributed process, 99.7% of the data points will fall within plus or minus three standard deviations from the mean. Here, three standard deviations equal 63 grams (21 grams x 3), thus the range of weights that 99.7% of the chocolates would fall into is from 454 grams to 580 grams (517 +/- 63 grams).

Since the customer's lower tolerance limit is 483 grams, and the Empirical Rule suggests that 99.7% of the chocolates will weigh more than 454 grams, this suggests that the capability of the current processes meets and exceeds the requirement set by the customer for the lower bound, and there is an allowance for heavier chocolates which the customers don't mind. Therefore, Lucullus Company's processes should conform to these requirements.