In the following random experiment, decide whether the random variable X is binomial or not:Approximately 1 in 10 people are left-handed. Let X be the number of people that are left-handed out of a random sample of 200 individuals. Although the individuals are sampled without replacement, it is assumed that we are sampling from such a vast population that the selections are virtually independent. Binomial Not binomial
Question
In the following random experiment, decide whether the random variable X is binomial or not:Approximately 1 in 10 people are left-handed. Let X be the number of people that are left-handed out of a random sample of 200 individuals. Although the individuals are sampled without replacement, it is assumed that we are sampling from such a vast population that the selections are virtually independent. Binomial Not binomial
Solution
The random variable X in this experiment can be considered as a binomial random variable. This is because the experiment meets the four conditions required for a binomial experiment:
- The experiment consists of a fixed number of trials (200 individuals are sampled).
- Each trial is independent (it is stated that the selections are virtually independent).
- Each trial can result in just two possible outcomes (a person is either left-handed or not).
- The probability of success (finding a left-handed person) is the same for each trial (approximately 1 in 10).
So, the answer is Binomial.
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