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Which one of these variables is a binomial random variable? A. time it takes a randomly selected student to complete a multiple choice exam B. number of women taller than 68 inches in a random sample of 5 women C. number of CDs a randomly selected person owns D. number of textbooks a randomly selected student bought this term

User EkoJR
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1 Answer

3 votes

Answer:

The correct option is (B).

Explanation:

A Binomial experiment has the following properties:

  • There are a fixed number of trials (n).
  • Each trial are independent of the others.
  • Each trial has only two outcomes: Success and Failure
  • Each trial has the same probability of success (p).

If a random variable X is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.

Consider the random variable:

X = number of women taller than 68 inches in a random sample of 5 women

  • The number of trials is fixed, i.e. n = 5.
  • The heights of each women is independent of others.
  • The trials have only two outcomes: women taller than 68 inches and women not taller than 68 inches.
  • Each trial has the same probability of success, P (women taller than 68 inches)

Thus, the random variable, number of women taller than 68 inches in a random sample of 5 women is a binomial random variable..

Thus, the correct option is (B).

User Shannan
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