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.

Question

Mathematics

Tobias Key

15 July, 03:42

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.

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Valery Matthews · Answer 1

Since both conditions (only two outcomes, independent trials) are satisfied, the random variable X is binomial.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they are left-handed, or they are not. This is the first condition for the random variable X being binomial.

The selections are independent, that is, the probability of a person being left handed is independent from other people. This is the second condition for the random variable X being binomial.

Since both conditions (only two outcomes, independent trials) are satisfied, the random variable X is binomial.