Final answer:
This student's question deals with statistical analysis, including probability calculations and the determination of confidence intervals for given situations in a collegiate setting.
Step-by-step explanation:
The question relates to statistics and probability, and involves a number of scenarios asking for calculations based on given data. For instance, when looking at the probability of a senior taking a gap year or determining the confidence interval for the proportion of freshmen who have declared their majors at State University.
Using these scenarios, here are some statistical analyses:
- From the total of 200 seniors, with 140 going to college, 40 working, and the rest taking a gap year, we use the basic probability formula P(Event) = Number of ways event can occur / Total number of possible outcomes to find the probability of a senior taking a gap year.
- To find a 96 percent confidence interval for the freshmen who have declared their majors, we use the plus-four method, incorporating the number of students who have declared majors (31) out of the sample size (65).