SOLUTION: According to the college registrar's office, 50% of students enrolled in an introductory statistics class this semester are freshmen, 20% are sophomores, 20% are juniors, and 10% a
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Question 1053849: According to the college registrar's office, 50% of students enrolled in an introductory statistics class this semester are freshmen, 20% are sophomores, 20% 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?
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 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 "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.
Yes. This is a standard binomial probability model.
No. These trials are not independent.
No. There are more than two outcomes.
No. The probability of success is the same for each trial.
What other probability distribution would be more appropriate in this setting?
chi-square
uniform
normal
hypergeometric
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
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 a student enrolled in introductory statistics.
Yes we can model this trial with "freshman" being a success and "any other class" as a failure.
p = (.10*.50) = .05 , q = .95, n = 5
P( x = 2F) = binompdf(5,.05,5)
|
|sampling without replacement
30stdents: 15Sr, 6Jr , 6SO, 3Fr
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.
|
What other probability distribution would be more appropriate in this setting?
hypergeometric
P(X = 2Fr) = (3C2)(27C2)/(30C5)
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