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

As per the given information in the question

Pr(Freshmen) = 0.50

Pr (sophomore) = 0.20

Pr(Junior) = 0.15 ; Pr( Senior) = 0.15

Out of random sample of 5 studnets, we have to find the probability that 2 are freshmen.

(a) A Trial is  consists of looking at the class status of a student enrolled in introductory statistics.

Here we can model this as being " freshmen" is a success and being " other class" is failure.

Probability of success = 5C2 (0.5)2 (0.5)3 = 0.3125

(b) Here we are sampling without replacement and only 30 students are enrolled in statistics class. Is it appropriate to model 5 trials as independent.

ANswer : Here answer is No, as These trials are not independent.

(c) Here in this the more appropriate probability distribution is HYPERGEOMETRIC Distribution.

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