Question

In each of the following situations, is it reasonable to use a binomial distribution for the random variable XX? Give reasons for your answer in each case.

(a) A manufacturer of medical catheters randomly selects eight catheters, one from each hour's production for a detailed quality inspection. One variable recorded is the count XX of catheters with an unacceptable diameter (too small or too large).

A binomial distribution is reasonable. There is a fixed number of catheters produced each day, catheters of unacceptable diameter occur randomly and independently, there are two possible outcomes for each observation, and the probability of success is the same for each observation.

A binomial distribution is unreasonable. There are more than two outcomes: acceptable diameter, too small, or too large.

A binomial distribution is reasonable. The observations are not independent.

A binomial distribution is reasonable. One hour of production is a fixed interval of time, the number of catheters with unacceptable diameter occur randomly and independently over the hour, and the probably of producing a catheter of unacceptable diameter is constant throughout the day.

(b) A sample survey asks 100100 persons chosen at random from the adult residents of a large city whether they oppose the legalization of medical marijuana; XX is the number of people who say "yes."

A binomial distribution is unreasonable. Selecting an individual to participate in the survey changes the remaining proportion of adults that oppose the legalization of medical marijuana.

A binomial distribution is unreasonable. The sample size is too small compared to the population size.

A binomial distribution is reasonable. There is a fixed number of people surveyed. The survey is in a large city with a large population so the change in probability of a particular resident being opposed to medical marijuana legalization is negligible. There are only two outcomes, a person is either for or against the legalization of medical marijuana. The people surveyed were chosen at random so their opinions are independent of each other.

A binomial distribution is unreasonable. There are more than 2 outcomes: Yes, No, and non responsive.

(c) A pediatrician sees 24 unrelated children on one winter day. XX is the number of patients who came because of cold or flu symptoms.

A binomial distribution is unreasonable. There are more than 2 outcomes since there are several different kinds colds and flus.

A binomial distribution is unreasonable. The probability of seeing children with cold or flu symptoms is very variable.

A binomial distribution is unreasonable. The sample size is too small compared to the population size.

A binomial distribution is reasonable. There is a fixed number of children seen. There are only two outcomes, a patient who came because of cold or flu symptoms and those who did not. The children are unrelated so are independent of each other. During the winter time, the probability of a child having cold or flu symptoms should remain constant.

Answer 1

a) Ans :

A binomial distribution is reasonable.

There is a fixed number of catheters produced each day, catheters of unacceptable diameter occur randomly and independently, there are two possible outcomes for each observation, and the probability of success is the same for each observation.

b) Ans :

A binomial distribution is unreasonable.

Selecting an individual to participate in the survey changes the remaining proportion of adults that oppose the legalization of medical marijuana.

c) Ans :

A binomial distribution is unreasonable.

The probability of seeing children with cold or flu symptoms is very variable.