AI$-$generated answer

Scenario $1$: To determine whether "tanking" would be a good strategy for a baseball team exploring a rebuild through draft picks, you need to calculate where your team falls on the normal distribution of wins and identify the number of wins that would have placed them in the bottom $10\%.$ This analysis will help you assess whether the team would have qualified for the lottery for the first pick in the next season's draft.

First, you should use the data from the Major League Baseball seasons from $1962-2012$ to calculate the mean and standard deviation of wins for the league during the year you were born. Using the Z$-$score formula, you can then determine the percentile rank of your team in terms of wins. If your team falls in the bottom $10\%,$ it means they would have qualified for the draft lottery.

When evaluating whether "tanking" would be a good strategy, consider the ethical implications and long$-$term consequences for the team's reputation and fan base. While securing a high draft pick can be advantageous for future success, deliberately underperforming may harm the team's credibility and alienate fans. It's essential to weigh the potential benefits of a high draft pick against the negative impact on the team's morale and public perception.

In conclusion, the decision to "tank" should be made strategically and ethically, taking into account both the statistical analysis of the team's performance and the broader implications for the team's future success and reputation.