Question
To get full credit in this post, first, you need to state a binomial problem in your example. Then, you must explain that your selected
To get full credit in this post, first, you need to state a binomial problem in your example. Then, you must explain that your selected problem exhibits the four properties that define a binomial experiment. Below is an example of how you are expected to present your post. Of course, you would write your post using your own example and words.
Example.A pharmaceutical company advertises a drug as being preferred by 70% of all the doctors. Let's assume that this advertisement is true. Also, suppose that 12 doctors are chosen at random and interviewed about their preference for this drug.
This problem is binomial because it meets the four properties or conditions that define a binomial experiment, as illustrated below:
- The problem (or experiment) consists of a sequence of 12 identical trials. In this example, a trial represents interviewing each of the 12 doctors with the question, do you prefer this drug?
- Each trial (or interview) has only two possible outcomes. When one of the selected doctors is interviewed with the question, do you prefer this drug?, there will be only two possible answers: Yes or no.
- The probability of success, p, remains constant from trial to trial. In this problem, success means "the selected doctor prefers the drug." According to the problem, 70% of all the doctors prefer the drug. Then, the probability of success, p = 0.70, is constant from interview to interview.
- The trials are independent. It is clear that the successive trials (or interviews) are independent of each other because the answer provided by one of the 12 doctors is not going to affect the answers of the rest of the doctors in the sample.
Therefore, this problem is binomial withn = 12,p = 0.70, andq = 1 - p = 0.30.
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