Final answer:
The questions involve statistical analysis within the mathematics field, particularly focusing on sampling methods, probability, and inference from sample data in a workplace context.
Step-by-step explanation:
The questions presented are all related to the field of statistics, a branch of mathematics that involves collecting, analyzing, interpreting, presenting, and organizing data. In a workplace setting, statistics can be used to understand commuting patterns, the probability of events such as the number of long-distance calls made during peak times, and sampling methods for collecting data efficiently and effectively.
For instance, if Dani's office consists of 600 employees and she wishes to understand how they commute to work, she might create a table or use a tree diagram to categorize the different modes of transportation, such as walking alone, carpooling, or using other forms of transportation. If it is known what percent of the employees walk alone, those who drive alone, and those who carpool, then predictions can be made about how many out of a new sample, say 1,000 workers, would be expected to travel alone or carpool.
Another scenario given was related to a hypothesis test where two supervisors, Javier and Ercilia, each survey 100 shoppers to estimate the mean distance that shoppers live from the mall. This is an example of using sample data to make inferences about a larger population.