In each of the following situations, is it reasonable to see a binomial distribu

Question

In each of the following situations, is it reasonable to see a binomial distribution for the random variable X? Give reasons for your answer in each case. If a binomial distribution applies, give the values of n and p.

(a) In a random sample of 20 students in a fitness study, X is the mean daily exercise time of the sample.

(b) A manufacturer of running shoes picks a random sample of 20 shoes from the production of shoes each day for a detailed inspection. X is the number of pairs of shoes with a defect.

(c) A college tutoring center chooses an SRS of 50 students. The students are asked whether or not they have used the tutoring center for any sort of tutoring help. X is the number who say that they have.

(d) X is the number of days during the school year when you skip a class.

Explanation / Answer

(a) In a random sample of 20 students in a fitness study, X is the mean daily exercise time of the sample. This is not binomial as p is not same for all.

(b) A manufacturer of running shoes picks a random sample of 20 shoes from the production of shoes each day for a detailed inspection. X is the number of pairs of shoes with a defect.

This is binomial as p is same for all, n is constant, events are independent, and only two outcomes. Here n=20 and p=0.5

(c) A college tutoring center chooses an SRS of 50 students. The students are asked whether or not they have used the tutoring center for any sort of tutoring help. X is the number who say that they have.

This is binomial as p is same for all, n is constant, events are independent, and only two outcomes. Here n=50 and p=0.5

(d) X is the number of days during the school year when you skip a class.

This is not binomial as n is not constant.

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