It is known that 64% of Americans personally worry a great deal about federal sp
ID: 3150897 • Letter: I
Question
It is known that 64% of Americans personally worry a great deal about federal spending and the budget deficit. Which of the following needs to be satisfied in order to be able to use the Central Limit Theorem to describe the sampling distribution of the proportion of Americans who personally worry a great deal about federal spending and the budget deficit?
1.The sample needs to be random.
2.If sampling without replacement, the sample size needs to be less than 10% of the population size.
3.The sample size should not be less than 50.
4.The expected numbers of those who do and do not personally worry a great deal about federal spending and the budget deficit need to both be at least 10.
Pick one...
A.1, 2, and 4
B.1 and 3
C.1, 2, and 3
D.1, 2, 3, and 4
E.1 and 2
Explanation / Answer
It is known that 64% of Americans personally worry a great deal about federal spending and the budget deficit. Which of the following needs to be satisfied in order to be able to use the Central Limit Theorem to describe the sampling distribution of the proportion of Americans who personally worry a great deal about federal spending and the budget deficit?
1.The sample needs to be random.
2.If sampling without replacement, the sample size needs to be less than 10% of the population size.
3.The sample size should not be less than 50.
4.The expected numbers of those who do and do not personally worry a great deal about federal spending and the budget deficit need to both be at least 10.
Answer A
Pick one...
A.1, 2, and 4
B.1 and 3
C.1, 2, and 3
D.1, 2, 3, and 4
E.1 and 2
Binomial Distribution has 4 requirements:
1.The experiment must have a fixed number of trials
2.The trials must be independent
3.Each trial must have all outcomes classified into two categories
4.The probabilities must remain constant for each trial.
Normal approximation to the binomial distribution is appropriate when the number of observations n must be large enough, and the value of p so that both np and n(1 - p) are greater than or equal to 10.
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