A recent Gallup poll (Poll Analyses May 22, 2002) revealed that 81% of Americans

Question

A recent Gallup poll (Poll Analyses May 22, 2002) revealed that 81% of Americans say they have a credit card.  You randomly chose 12 Americans and ask if they have at least one credit card.

1.      Does this situation meet the binomial requirements? Why or why not?  Address the five characteristics in the Key Points.

2.      What is the random variable in this problem? i.e., what does X represent and what values can it have?)

3.      What is the probability that exactly 9 have credit cards?

4.      What is the probability that 7 or fewer have credit cards?

5.      What is the probability that at least 10 have credit cards?

6.      What is the probability that at most 10 have credit cards?

7.      What is the mean number of adults out of a sample of 12 that you would expect to have credit cards?  What is the standard deviation of the distribution?

Explanation / Answer

A binomial experiment is a probability experiment that satisfies the following four requirements: 1. Each trial can have only two outcomes or outcomes that can be reduced to two outcomes. These outcomes can be considered as either success or failure. 2. There must be a fixed number of trials. 3. The outcomes of each trial must be independent of each other. 4. The probability of a success must remain the same for each trial. Yes this meets our all the requirements of Binomial Experiment Because :- 1) Two Outcomes (81% Success and 19% Failure) 2)Fixed Trials (12) 3)All are independent 4)Probability same (0.81 for all the 12 people)

//The question is lengthy for 750 points

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