Question

Which of the following scenarios does NOT represent a binomial variable?

a) An SRS of 22 widgets are picked from a production line and inspected. X represents the number of defectives produced.

b) A coin is flipped until heads comes up the first time. X represents the number of rolls required.

c) A fair die is rolled 10 times. X represents the number of times 5 comes up.

d) An SRS of 120 students are asked, Do you love baseball? X represents the number of yes answers received.

Answer 1

Option b) A coin is flipped until heads comes up the first time

Step-by-step explanation:

The scenario that does NOT represent a binomial variable is option b) A coin is flipped until heads comes up the first time. X represents the number of rolls required.

In a binomial variable, there are three characteristics that need to be met:

1. There must be a fixed number of trials.
2. Each trial must have only two possible outcomes, referred to as success and failure.
3. The trials must be independent and performed under identical conditions.

In this scenario, the number of trials is not fixed, as the number of coin flips required for heads can vary. Therefore, it does not meet the criteria for a binomial variable.