Is It a Binomial Experiment? No Can It Be Reduced To Binomial Experiment? Yes Trial: Asking families Random Variable: Number of land line telephones
n: 55
p: 0.20
q: 0.80
Each trial has only two possible outcomes — success or failure.
The probability of success p is the same in every trial. The probability of failure q is 1-p.
The random variable X is the number of successes in n trials.
Let's now consider the given experiment to determine whether it is a binomial experiment or can be reduced to a binomial experiment.
A study finds that 20 % of families in a town have a land line telephone. You ask 55 families how many land line telephones do they have.
Each family can respond with a non-negative integer number. Therefore, there are more than two possible answers. In a binomial experiment we require that there are exactly two available answers. This means that this experiment is not binomial.
Possible answers:
0 , 1 , 2 , 3 , 4 , 5 , ...
However, it all depends how we perceive the answer. To verify the study mentioned, it is sufficient to distinguish only two possibile answers, zero and at least one land line telephones. Therefore, we can reduce this experiment to a binomial experiment.
Possible answers: 0 , 1 , 2 , 3 , 4 , 5 , ..._(At least one)
By doing this, we only have two possible answers, which are zero lines and at least one line. Recall that 20 % written as a decimal is 0.2. Therefore, when we ask if the family has a land line telephone, we can think of the responses as having the following probabilities.
Response
Variable
Probability
At least one line.
p
0.2
Zero lines.
1- p= q
1- 0.2= 0.8
Let's see if now the experiment satisfies the conditions to be a binomial experiment.
Condition
Explanation
Is it Satisfied?
1.
Each trial is asking the question to a singular family in town teacher. There is a fixed number of independent trials, n=55.
✓
2.
Success is At least one, failure is Zero
✓
3.
The probability of success is the same in every trial, p=0.2. The probability of failure is q=0.8.
✓
4.
The random variable X is the number of At least one responses.
✓
Since the experiment satisfies the conditions, it is a binomial experiment.
