Answered

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The National Survey on Drug Use and Health also reported that 21% of males in the same age group (12-20) are binge drinkers. Suppose that in addition to the 10 randomly chosen females, a random sample 10 males from the same age group is chosen (to a total of 20). Let the random variable Y be the total number of males and females (out of 20) who are binge drinkers. Which of the following is true regarding the random variable Y?
a. Y has a binomial distribution with n-60 and p.16
b. Y does not have a binomial distribution since p, the probability of being a binge drinker, is not the same for all the trials.
c. Y has a binomial distribution with n-60 and p .31
d. Y does not have a binomial distribution since the number of trials n is not fixed.
e. Y does not have a binomial distribution since the trials are not independent.

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Answer:

Y does not have a binomial distribution since p, the probability of being a binge drinker, is not the same for all the trials.

Step-by-step explanation:

For a binomial distribution, condition required include :

A fixed number of trials ; Here the number of trials is 20 ; hence, this condition is met.

Each trial must be independent : yes, it is independent as a selected individual could either be a binge drinker or not. The outcome of each trial is either a success or a failure ; being a drinker or not.

However, the probability of being a binge drinker (that is probability of success) could vary for male and female. The probability of male being a binge drinker is 0.21 while that if female isn't specified, this probability, p value should be the same for all trials. Hence, with this value not being the same for all trials, the binomial probability condition is violated.

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