Binomial setting? A binomial distribution will be approximately correct as a model for one of these two settings and not for the other. Explain why by briefly discussing both settings. (a) When an opinion poll calls residential telephone numbers at random, only $20\%$of the calls reach a person. You watch the random digit dialing machine make $15$calls. $X$is the number that reaches a person

(b) When an opinion poll calls residential telephone numbers at random, only $20\%$of the calls reach a live person. You watch the random digit dialing machine make calls. $Y$is the number of calls until the first live person answers

Given that an opinion poll calls residential telephone numbers at random,

only $20\%$of the calls reach a person.

We watch the random digit dialing machine make $15$calls. $X$is the number that reaches a person

The variable $X$ in this question has a binomial distribution since each subsequent draw is independent of the preceding draw because success is defined as the number reaching a person. The maximum number of calls is set at $15$. The chance of success remains constant at $20\%$. Because the numbers are chosen at random, each draw can be considered independent.

Given that an opinion poll calls residential telephone numbers at random,

only $20\%$of the calls reach a live person. $Y$is the number of calls until the first live person answers

Because there is no set number of components being drawn, the binomial distribution will not be able to produce a good estimate in this case. In anticipation of the first real individual answering, a draw is made.