According to the college registrar\'s office, 50% of students enrolled in an int

Question

According to the college registrar's office, 50% of students enrolled in an introductory statistics class this semester are freshmen, 20% are sophomores, 15% are juniors, and 15% 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?

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.
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.
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.
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.

What is the probability of success?

(b) 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? Explain.

No. These trials are not independent.No. There are more than two outcomes.    No. The probability of success is the same for each trial.Yes. This is a standard binomial probability model.

What other probability distribution would be more appropriate in this setting?

normalhypergeometric    uniformchi-square

Explanation / Answer

a) To determine the probability that in a random sample of five students

enrolled in introductory statistics this semester,

That is trials = sample size = n = 5

Yes we  can model a trial as having only two outcomes

Success is the students enrolled in an introductory statistics class this semester are freshmen

and failure is the students enrolled in an introductory statistics class this semester are not freshmen

So correct option is

"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."

According to the college registrar's office, 50% of students enrolled in an introductory statistics class this semester are freshmen,

So probability of success = 0.50

P(Exactly 2 are freshman) = "BINOMDIST(2,5,.5,0)" = 0.3125

b) Since sampling is done without replacement so probability of trials depend on previous trials

therefor trials are not independent

So correct option is "No. These trials are not independent."

For n is fixed and sampling is done without replacement then we used Hypergeometric distribution

So correct option is Hypergeometric distribution.

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