Probability Analysis: Which Seamstress Is More Likely to Complete the Task by 8:25 AM?

In the fashion industry, efficiency and timely completion of tasks are crucial for seamstresses working on intricate designs and patterns. This article delves into a specific scenario involving two seamstresses, Marcela and Lorenza, to determine which one has a better chance of completing a cloth pattern by a specified deadline. By analyzing the expected completion times, we can gain insights into the probability of each seamstress finishing the task successfully.

Introduction to Seamstresses

Marcela and Lorenza are experienced seamstresses known for their meticulous work. Their estimated time to cut a cloth pattern is as follows:

Marcela: 20 to 40 minutes Lorenza: 15 to 45 minutes

Both seamstresses start their work at 8:00 AM. The critical question is whether they will have a higher probability of completing the task by 8:25 AM. To answer this, we need to conduct a probability analysis taking into account the variation in their cutting times.

Assumptions and Analysis

For the purposes of this analysis, we will make the following assumptions:

The exact time each seamstress takes to cut the cloth pattern is uniformly distributed within their respective ranges. The time allowed to complete the task is 25 minutes (from 8:00 AM to 8:25 AM).

Marcela's Probability of Completion

Marcela's estimated time range is 20 to 40 minutes. We need to determine the probability that she will complete the task within the 25-minute window.

If Marcela's cutting time is X minutes, the favorable outcome is that X is between 20 and 25 minutes.

The favorable range for Marcela is:

25 minutes (end of the task) - 20 minutes (start of the range) 5 minutes

The total range of possible time for Marcela is:

40 minutes (end of the range) - 20 minutes (start of the range) 20 minutes

Thus, the probability that Marcela will complete the task within the 25-minute window is:

5/20 0.25 or 25%

Lorenza's Probability of Completion

Lorenza's estimated time range is 15 to 45 minutes. We need to determine the probability that she will complete the task within the 25-minute window.

If Lorenza's cutting time is Y minutes, the favorable outcome is that Y is between 15 and 25 minutes.

The favorable range for Lorenza is:

25 minutes (end of the task) - 15 minutes (start of the range) 10 minutes

The total range of possible time for Lorenza is:

45 minutes (end of the range) - 15 minutes (start of the range) 30 minutes

Thus, the probability that Lorenza will complete the task within the 25-minute window is:

10/30 0.33 or 33.33%

Conclusion

Based on the probability analysis, Lorenza has a higher probability of completing the cloth pattern by 8:25 AM compared to Marcela. The probability that Lorenza will finish within the 25-minute window is 33.33%, while Marcela's probability is 25%.

Note: This analysis relies on the given assumptions and the uniform distribution of cutting times. In real-world scenarios, other factors such as the complexity of the pattern or environmental conditions can significantly affect the actual completion times.

Keywords: probability analysis, seamstress, completion time