Problem:
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.
Required:
Question 1: Does this situation meet the binomial requirements? Why or why not? Address the five characteristics in the Key Points.
Question 2: What is the random variable in this problem? i.e., what does X represent and what values can it have?)
Question 3: What is the probability that exactly 9 have credit cards?
Question 4: What is the probability that 7 or fewer have credit cards?
Question 5: What is the probability that at least 10 have credit cards?
Question 6: What is the probability that at most 10 have credit cards?
Question 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?
Note: Please provide reasons to support your answer.