Final answer:
The Altman Z-score predicts bankruptcy risk and higher z-scores indicate a better financial position; thus, John is better positioned than Ali. The Empirical Rule outlines percentages of data within standard deviation ranges. Z-scores can compare different data sets by showing the distance from their means in standard deviations.
Step-by-step explanation:
The Altman Z-score is a financial formula that can be used to predict the likelihood of a company going bankrupt within two years. Calculating the Z-score requires several financial ratios and balance sheet values. In comparing John's z-score and Ali's z-score, we determine that a higher z-score indicates a better financial position. John's z-score of -0.21 implies a better position than Ali's z-score of -0.30, as John's z-score is closer to the mean.
The Empirical Rule, also known as the 68-95-99.7 rule, relates to z-scores in the context of a normal distribution. It states that approximately 68% of data within a normal distribution falls between z-scores of -1 and 1, about 95% between z-scores of -2 and 2, and about 99.7% between z-scores of -3 and 3. The comparison of different z-scores and their corresponding percentages of data falling within those ranges provides an understanding of how individual values relate to the distribution as a whole.
When comparing values from different data sets, especially with different means and standard deviations, z-scores are indispensable. They allow us to understand how many standard deviations a value is from the mean. In the context of the examples provided, measuring the difference between company average retention times could involve calculating the z-scores for Company A and Company B, and then comparing these values to determine which company tends to retain workers longer.