Question

In each of the following cases, decide whether a binomial distribution is an appropriate model, and give your reasons.

1. A firm uses a computer-based training module to prepare 20 machinists to use new numerically controlled lathes. The module contains a test at the end of the course; X is the number who perform satisfactorily on the test.

2. The list of potential product testers for a new product contains 100 persons chosen at random from the adult residents of a large city. Each person on the list is asked whether he or she would participate in the study if given the chance; X is the number who say "Yes".

3. Either in a job you currently have or one that you would like to have, describe a data set you could collect that would be in the binomial setting.

Answer 1

Answer:

1)

Each participant will perform independently, there are only two outcomes: The individuals will perform satisfactory (x) or not, each participant has the same the probability of satisfactory performance, therefor binomial distribution is an appropriate model

2)

In this case, Binomial distribution consists of n repeated trials and there are only be two outcomes, “yes” or “no”. The probability of success is the same on every trial. The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials. The conditions are satisfied and binomial distribution is an appropriate model.

3)

As a recruiter for Engineers for the Federal Government, to be eligible an individual must have a degree from an ABET approved college. To consider eligibility, we would ask if the individual had completed their degree at an ABET college. If the answer was “yes” they were eligible, if “no”, then they were not eligible. In this case, Binomial distribution consists of n repeated trials and there are only be two outcomes, “yes” or “no”. The probability of success is the same on every trial. The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials. The conditions are satisfied and binomial distribution is an appropriate model.

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