Which of the variables meet the conditions for a binomial di

Which of the variables meet the conditions for a binomial distribution? Select all that apply.

A. The number of people in a family of size 4 who go to church on a given Sunday, when any one of them goes 50% of the time in the long run.

B. The number voting for the Democratic candidate out of the 100 votes in the first precinct that reports results, when 60% of the population voted for the Democrat.

C. The number of females in a random sample of 4 students from a class of size 20, when half the class is female.

D. The number with iron deficiency in a random sample of 3 adolescent girls from the United States, when 10% of adolescent girls have iron deficiency.

E. The number belonging to the rotary club in a random sample of 10 people from a service organization with 204 members, when 50 of the members of the service organization belong to the rotary club

Solution

Conditions for Binomial Distribution:

a) No. Each trial does not seem independent because if one member of a family is going to church can influence other family members also.

b) No. The probability of voting for the Democratic candidate cannot be same in each precinct.

c) No. Sample is not independent because sample size is more than 10% of the population size.

d) Yes. This satisfies all three conditions with n=3 and p=0.1.

e) No. Probability of success is not same.