Final answer:
The standard deviation of the cereal box weights is greater than the acceptable limit of 0.5 ounces. Hence, the equipment may need recalibration to ensure the weights are maintained within the desired specifications. This mirrors the significance of small differences as outlined by the concept of JND in Weber's Law.
Step-by-step explanation:
When determining whether the equipment used for packaging requires recalibration, the weights of the products are crucial. In the scenario presented, the plant manager has noted that the standard deviation of the cereal box weights is 0.54 ounces, which is greater than the desired maximum of 0.5 ounces. This indicates the machine may indeed need recalibration.
The process to determine the need for recalibration is to observe if the actual standard deviation exceeds the acceptable threshold. Considering that the acceptable threshold for standard deviation is at most 0.5 ounces, and the observed standard deviation from a sample of 84 cereal boxes is 0.54 ounces, this exceeds the acceptable limit. Therefore, it is advisable for the plant manager to recalibrate the machine to ensure the weights are within the expected range.
Comparing this to the concept of Just-Noticeable Difference (JND) from Weber's Law, we can understand that even small deviations in weights can be significant, depending on the context and requirements of accuracy.