According to the college registrar's office, 45% of students enrolled in an introductory statistics class this semester are freshmen, 20% are sophomores, 25% are juniors, and 10% are seniors. You want to determine the probability that in a random sample of five students enrolled in introductory statistics this semester, exactly two are freshmen. (a) Describe a trial. Can we model a trial as having only two outcomes? If so, what is success? What is failure? Choose one of the statements below: A. A trial consists of looking at the class status of a student enrolled in introductory statistics. Yes we can model this trial with "freshman" being a success and "any other class" as a failure. B. A trial consists of looking at the class status of a student enrolled in introductory statistics. Yes we can model this trial with "junior" being a success and "any other class" as a failure. C. A trial consists of looking at the class status of a student enrolled in introductory statistics. Yes we can model this trial with "sophomore" being a success and "any other class" as a failure. D. A trial consists of looking at the class status of all students. Yes we can model this trial with "freshman" being a success and "any other class" as a failure. (b) What is the probability of success? (c) We are sampling without replacement. If only 30 students are enrolled in introductory statistics this semester, is it appropriate to model 5 trials as independent, with the same probability of success on each trial? Choose one of the statements below: A. No. There are more than two outcomes. B. No. These trials are not independent. C. No. The probability of success is the same for each trial. D. Yes. This is a standard binomial probability model.
According to the college registrar's office, 45% of students enrolled in an introductory statistics class this semester are freshmen, 20% are sophomores, 25% are juniors, and 10% are seniors. You want to determine the probability that in a random sample of five students enrolled in introductory statistics this semester, exactly two are freshmen.
(a) Describe a trial. Can we model a trial as having only two outcomes? If so, what is success? What is failure? Choose one of the statements below:
A. A trial consists of looking at the class status of a student enrolled in introductory statistics. Yes we can model this trial with "freshman" being a success and "any other class" as a failure.
B. A trial consists of looking at the class status of a student enrolled in introductory statistics. Yes we can model this trial with "junior" being a success and "any other class" as a failure.
C. A trial consists of looking at the class status of a student enrolled in introductory statistics. Yes we can model this trial with "sophomore" being a success and "any other class" as a failure.
D. A trial consists of looking at the class status of all students. Yes we can model this trial with "freshman" being a success and "any other class" as a failure.
(b) What is the probability of success?
(c) We are sampling without replacement. If only 30 students are enrolled in introductory statistics this semester, is it appropriate to model 5 trials as independent, with the same probability of success on each trial? Choose one of the statements below:
A. No. There are more than two outcomes.
B. No. These trials are not independent.
C. No. The probability of success is the same for each trial.
D. Yes. This is a standard binomial probability model.
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