Final answer:
Gale's science grade could be determined by various components including class activity, homework, tests, and attendance, but with a collective grading model, all students get a 'C' based on a class mean. To define the number of students doing homework on time (X), we consider a binomial distribution where X is the count of successes in the class.
Step-by-step explanation:
Gale's grade in science for the term is typically determined by a combination of factors such as class participation, homework completion, exams and projects, and attendance. However, if the teacher chooses to use a collective grading model, as in the example where every student receives a "C" because the class mean was 75%, this would reflect the teacher's decision to grade students equally based on the average performance of the class, which the teacher could view as a fairer or more communal approach.
In the scenario where we want to define X as the number of students who do their homework on time, we would be dealing with a binomial distribution where X represents the number of successes (in this case, students doing their homework on time) out of a fixed number of trials, with each trial being independent and having the same probability of success (p = 0.70). Assuming the class size is 50, and we want to find the probability that at least 40 students do their homework on time, we would calculate this using the binomial distribution formula.