1 Which of the following lead to binomial distributions Expl

1.     Which of the following lead to binomial distributions? Explain
a. An inspection procedure at an automobile manufacturing plant involves selecting a   
    sample of cars from the assembly line and noting for each car whether there are no
    defects, at least one major defect, or only minor defects.
b. As students study more and more during statistics class, their chances of getting an A
    on any given test continue to improve. The professor is interested in the probability of    
    any given student receiving various numbers of A’s on the class exams.
c. A committee of two is to be selected from among the five teachers and ten students
    attending a meeting. What are the probabilities that the committee will consist of two
    teachers, of two students, or of exactly one teacher and one student.

2.     Suppose USAir accounts for 20% of all U.S domestic flights. As of mid-1194, USAir was involved in four of the previous seven major disasters. “That’s enough to begin getting suspicious but not enough to hang them,” said Dr. Brad Efton in The New York Times (September 11, 1994, Sec 4, p. 4). Using a binomial distribution, comment on Dr. Efton’s remark.   

Solution

As multiple questions are posted, only the first one will be answered.

1. Answer : b

This is because, for any particular student, there will be \'n\' number of exams where he/she has the probability \'p\' of getting Grade A in each exam. So number of A grades follows a Binomial (n,p) distribution, where probability p is same for all exams taken by that student and exam grades are independent of each other.

In a. there are 3 outcomes of each trial, so outcome is not binary.

In c. again there are multiple ways of selecting the committee, so possible outcomes are not binary.