Question

Determine whether or not the given procedure results in a binomial distribution. For those that are not binomial, identify at least one requirement that is not satisfied.

a) Treating 863 subjects with Lipitor (Atorvastatin) and recording whether there is a "yes" response when they are each asked if they experienced a headache.
b) Treating 863 subjects with Lipitor (Atorvastatin) and asking each subject "How does your head feel?"
c) Twenty different Senators are randomly selected from the 100 Senators in the current Congress, and each was asked whether he or she is in favor of abolishing estate taxes.
d) Fifteen different Governors are randomly selected from the 50 Governors currently in office and the sex of each Governor is recorded.

Answer 1

a

This procedure results in a binomial distribution

b

This procedure would not results in a binomial distribution

c

This procedure results in a binomial distribution

d

This procedure would not results in a binomial distribution

Explanation:

A procedure must meet the following requirement in order for it to result in a binomial distribution

• The procedure trials must be independent
• Outcome of individual trials can be classified into two categories
• Success probability must remain the same in all trials
• The number of trials is fixed

Considering the first procedure we can see that it satisfies the requirement of above especially the requirement that the possible outcome of every trial is two

Considering the second procedure we see that would not results in a binomial distribution because the outcome of it trials cannot be classified into two categories

Considering the third procedure we can see that it satisfies the requirement of above especially the requirement that the trial must be independent

Considering the second procedure we see that would not results in a binomial distribution because there is no defined probability of success or failure