Chapter 1. Binomial Distributions in Statistical Sampling

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Questions 1-2

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Question 1.1

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Correct. If 37% are minorities, 100% – 37% = 63% are not minorities. Because we are selecting one student at random, the probability of selecting a non-minority is 63%, or 0.63.
Incorrect. If 37% are minorities, 100% – 37% = 63% are not minorities. Because we are selecting one student at random, the probability of selecting a non-minority is 63%, or 0.63.
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Question 1.2

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Correct. 25% of all students have grade point averages at least 3.0; however, are all students equally likely to be at the library on Friday evening? It is reasonable to assume that students at the library Friday evening are more studious than most, but it is impossible to say what the proportion of those with GPAs at least 3.0 would be.
Incorrect. 25% of all students have grade point averages at least 3.0; however, are all students equally likely to be at the library on Friday evening? It is reasonable to assume that students at the library Friday evening are more studious than most, but it is impossible to say what the proportion of those with GPAs at least 3.0 would be.
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Questions 3-4

3:33

Question 1.3

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Correct. Fun size bags are small. Drawing four from the bag will noticeably change what remains. This is the same situation as taking a handful from a small bowl in your kitchen.
Incorrect. Fun size bags are small. Drawing four from the bag will noticeably change what remains. This is the same situation as taking a handful from a small bowl in your kitchen.
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Question 1.4

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Correct. This would be an approximately binomial situation. Children are either part of a set of twins (or not), the proportion in the overall population is fixed, and we are taking a small sample relative to the size of the school.
Incorrect. This would be an approximately binomial situation. Children are either part of a set of twins (or not), the proportion in the overall population is fixed, and we are taking a small sample relative to the size of the school.
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