A telephone survey of Canadian families is conducted to determine the number of children in the average Canadian family. Past experience has shown that 30% of the families who are telephoned will refuse to respond to the survey. Which of the following data could NOT be classified as a binomial random variable?
A) the number of families out of 50 who respond to the survey
B) the number of families out of 50 who refuse to respond to the survey
C) the number of children in a family who respond to the survey

Question

Quizplus · Accepted Answer

A binomial random variable must have the following characteristics:
1. The experiment consists of a fixed number of trials.
2. Each trial is independent.
3. There are only two possible outcomes: success or failure.
4. The probability of success remains constant for each trial.
Option A and B meet all of these criteria as we are counting the number of successes (families who respond) out of a fixed number of trials (50) with a constant probability of success (70%). However, option C does not meet the criteria as the number of children in a family is not a binary outcome, it can take on any non-negative integer value.

A Telephone Survey of Canadian Families Is Conducted to Determine