Question

Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Surveying 2828 people to determine which statistics courses they have taken.

Answer 1

No, the given procedure doesn't result in binomial distribution.

Explanation:

For any procedure to be a binomial distribution, these below four conditions should be met;

Condition 1: Each and every observation should be independent from the other observations.

Condition 2: The probability of success(p) should always be same for each trial.

Condition 3: Number of trials(n) must be fixed.

Condition 4: There must be only two outcomes success or failure.

Now, the procedure given to us is : Surveying 2828 people to determine which statistics courses they have taken.

In this procedure;

• Condition 1 is satisfied since each observation is independent from other.

• Condition 3 is satisfied as n is fixed for surveying 2828 people.

• Condition 4 is not satisfied because there can be more than 2 answers from the people regarding which statistics courses they have taken as there as many statistics courses.

Answer 2

No, the given procedure doesn't result in a binomial distribution.

Explanation:

We can identify if a given procedure results in binomial distribution by observing whether these four conditions are met or not.

Condition 1: Each observation should be independent, it must not depend on the result of previous observation.

Condition 2: The probability of success should stay same from trial to trial.

Condition 3: n is fixed (the number of observations)

Condition 4: There are only two outcomes success or failure.

Surveying 2828 people to determine which statistics courses they have taken.

Condition 3 is satisfied since n is fixed

Condition 1 is satisfied since each observation is independent

Condition 4 is not satisfied since there can be more than 2 answers from the people (statistics courses can be many).