Question

For each of the following. explain whether it would be appropriate to use a binomial random variable.

a. In an effort to reduce traffic collisions, the department of transportation is studying the number of accidents that occur near a particular intersection. In the past year, traffic accidents have been reported at the location on 6 different days. The department is interested in the number of days that can be expected to elapse without an accident at the location.

b. Your company interviews 12 candidates for a position, and they call back candidates for second Interviews F they answer the interview questions to the satisfaction of all the interviewers. They hope to all back at least 3 because experience suggests an average of about 1 call back per 4 interviews.

c. A tennis instructor has 15 students. As she tracks their progress, she finds that about 86.5% of her students have improved their performance since their first lesson. Seeking to improve student performance the instructor decides to try out a new set of tennis drills on all 15 of her students. She decides to have all 15 students perform the drills, but the number who will improve as a result is not known in advance.

Answer 1

A binomial random variable is used to model processes that can assume one of the two values. A process that has more than two values cannot be modeled using a binomial random variable.

a) The number of accidents is being studied. The goal is to model the number of days passed before an accident occurs. An accident can either take place or it can't. Thus, there are only two possibilities for the event taking place. Hence, this can be modeled using a binomial random variable.

b) The candidates for the interview can either come back or they would not come back. Hence there are two possibilities for each candidate. Therefore, this process can be modeled using a Binomial process.

c) A student can either improve the drill or will not. Therefore, the process can be modeled using a binomial random variable. Therefore the process can be modeled using a Binomial random variable.