(30 points) In a class of 20 students, the professor calls on one student random
ID: 3062298 • Letter: #
Question
(30 points) In a class of 20 students, the professor calls on one student randomly to answer each question. The callings are independent from each other. That is, the probability for a given student being called for each question is 0.05. There are 10 questions in the next review session. (Identify the distribution first for each of the following questions except e.) 3. a) What is the probability that a given student is called upon 2 times during the term b) What is the probability that the first time a given student gets called is the 4 question? c) What is the probability that the scond time a given student gets called is the S question? d) Suppose there are 12 girls and 8 boys in the class. What is the probability that among the 10 questions, five are answered by girls? e) If the professor does not call the same student more than once in the review session. What is the probability a given student is called? 1t Please re-answer Question (d), considering the new information in Question (e).Explanation / Answer
Question 3 (a) The distribution is binomial where parameters n = 10 and p = 0.05
Pr(X = 2; 10 ; 0.05) = 10C2 (0.05)2 (0.95)8 = 0.0746
(b) The distribution is geometric here where the parameter p = 0.05
Pr(x = 4) = (1 - 0.05)3 * 0.05 = 0.0429
(c) The distribution is negative binomial one.Where n = 8 and p = 0.05
Pr(k = 2) = NB(k = 2; n = 8 ; 0.05) = 7C1 (0.95)6 * (0.05)2 = 0.01286
(d) Here the distribution is Binomial distribution again as all events are independent
so n = 10 and p = 12/20 = 0.6
Here Pr(X = 5) = BINOMIAL ( x = 5 ; 20 ; 0.6)= 0.200
(e) Professor does not call the same student more than once in the review session so
Pr(a student is called) = 10/20 = 0.50
(f) Nobody is asked same question twice so there is no replacement so distribution is hypergeometric distribution
N = 20 ; K = 12 ; n = 10
Pr(x = 5) = HYPGEOMETRIC (x = 5 ; 10 ; 12 ; 20) = 12C58C5/20C10 = 0.24
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.