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).