5.50 Should you use the binomial distribution? In each of the following situatio

Question

5.50 Should you use the binomial distribution? In each of the following situations, is it reasonable to a binomial distribution for the random variable X? Giu ive reasons for your answer in each case (a) In a random sample of 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 nutrition study chooses an SRS of college students. They are asked whether or not they usually eat at least five servings of fruits or vegetables per day. X is the number who say that they do. (d) X is the number of days during the school year when you skip a class

Explanation / Answer

For a binomial distribution,

Trials are independent. Probabilty of success remains same from one trial to another. And each trial has only two possible outcomes.

(A)

Mean daily time can be vary from one day to another. And trials are not independent. SO it is not a binomial distribution.

(B)

Each shoes can be defective or not. Shoes are independent from each other. Defective rate should be same from one day to another.

Hence, it is binomial experiment.

(C)

Each person can answer yes or no. Persons are independent from each other. Probability of success is 0.5 which is fixed from one trial to another.

Hence, it is binomial experiment.

(D)

Number of days you skip a class may vary from one year to another. So it is not an binomial experiment.

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