Chapter 6.3, Problem 51PB

Binomial assumptions For the following random variables, explain why at least one condition needed to use the binomial distribution is unlikely to be satisfied.

1. a. X = 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 (binomial, n = 4, p = 0.50). (Hint: Is the independence assumption plausible?)
2. b. X = 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 in that state (binomial, n = 100, p = 0.60). (Hint: Is the probability of voting for the Democratic candidate the same in each precinct?)
3. c. X = number of females in a random sample of four students from a class of size 20, when half the class is female (binomial, n = 4, p = 0.50).