. For each of the following questions, say whether the random process is reasona
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Question
. For each of the following questions, say whether the random process is reasonably a binomial process or not, and explain your answer. As part of your explanation, you will want to comment on the potential validity of each of things that must be true for a process to be a binomial process. If it is a binomial process, identify n : the number of Bernoulli trials and the probability of success.
(a) A fair die is rolled until a 1 appears, and X denotes the number of rolls.
(b) Ten different basketball players each attempt 1 free throw and X is the total number of successful attempts.
(c) It has been reported that nation-wide, one-third of all credit card users pay their bills in full each month. Let X be the number of people in a sample of 25 randomly chosen credit card users in Madison who pay their bill in full on a given month.
(d) Let X be the number of months out of a randomly chosen year that one randomly chosen credit card user in Madison pays their bill in full.
Explanation / Answer
A) No this is not a binomial process. In a fair die probability of 1 occurring is 1/6 but in a binomial process n must be a finite number. We do not know 1 occurs and the number of trials observed so it is not a binomial process.
B) No this is not a binomial process because even though each event is independent of the other as one player's successful or unsuccessful throw does not affect the others chance and we have total n events, the probability of each person's throw cannot be assumed to be the same. In a binomial distribution the probability of success for each trial must be the same.
C) Yes this is a binomial process. We have n= 25 and probability of success Is 1/3. It is binomial as the events are independent and probability of success of each event is the same and n is finite.
D) We have n = 12. Again like part b) above since the probability of paying the bill of the different card users is not given it cannot be assumed to be the same and the binomial assumption will not be valid. (If however this is connected to part c above then our probability is 1/3 and it will be valid).
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