Final answer:
A z-score is used to measure how far a data point is from the mean in terms of standard deviations. For waiting times at Supermarket A, Rosa's z-score is 1, and Binh's is -2. For stocking levels, a z-score of 1.28 corresponds to a 90% product availability rate.
Step-by-step explanation:
The z-score is a statistical measurement that describes the relation of a data point to the mean of a group of data points. In the context of stocking levels, if the mean waiting time at Supermarket A is 5 minutes with a standard deviation of 2 minutes, Rosa's 7-minute wait would result in a z-score of 1 because (7 - 5) / 2 = 1. This indicates Rosa waited one standard deviation longer than the average customer. Similarly, Binh's 1-minute wait would have a z-score of -2, calculated as (1 - 5) / 2 = -2, meaning Binh waited two standard deviations less than the average customer.
When analyzing stocking levels, a z-score of approximately 1.28 is used to calculate a stocking level that ensures product availability 90% of the time, as this z-score corresponds to an area under the normal curve to the left of z (the larger portion) of approximately 0.9, based on a z-table.