n 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.Group of answer choicesNot binomialBinomial
Question
n 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.Group of answer choicesNot binomialBinomial
Solution
The random variable X in this experiment is binomial. This is because the experiment meets all the conditions for a binomial distribution:
- The number of trials (n) is fixed (200 individuals are sampled).
- Each trial is independent (it is assumed that we are sampling from such a vast population that the selections are virtually independent).
- There are only two possible outcomes in each trial (a person is either left-handed or not).
- The probability of success (p) is the same for each trial (approximately 1 in 10 people are left-handed).
Therefore, the distribution of X is binomial.
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