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# Binomial Distributions, Geometric Distributions, and Sampling Distributions Multiple Choice Practice Problems for AP Statistics (page 2)

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By — McGraw-Hill Professional
Updated on Feb 4, 2011

### Solutions

1. The correct answer is (a).
2. The correct answer is (c). If it is a binomial random variable, the probability of success, p, is the same on each trial. The probability of not succeeding on the first trial and then succeeding on the second trial is (1 – p)(p). Thus, (1 – p)p = 0.25. Solving algebraically, p = 1/2.
3. The correct answer is (c). Although you probably wouldn't need to use a normal approximation to the binomial for small sample sizes, there is no reason (except perhaps accuracy) that you couldn't.
5. For small samples, the shape of the sampling distribution of will resemble the shape of the sampling distribution of the original population. The shape of the sampling distribution of is approximately normal for n sufficiently large.

6. The correct answer is (d). Because the problem stated "at least 10," we must include the term where x = 10. If the problem has said "more than 10," the correct answer would have been (b) or (c) (they are equivalent). The answer could also have been given as .
7. The correct answer is (d). .
8. The correct answer is (a).
9. The correct answer is (b). This is a characteristic of a binomial experiment. The analogous characteristic for a geometric experiment is that there is a random variable X that is the number of trials needed to achieve the first success.
10. The correct answer is (c). This is actually a binomial situation. If X is the count of students "in favor," then X has B(200, 0.70). Thus, P(X ≥ 150) = P(X = 150) + P(X =151) +… + P(X = 200). Using the TI-83/84, the exact binomial answer equals 1–binomcdf (200,0.7.0,149)= 0.0695. None of the listed choices shows a sum of several binomial expressions, so we assume this is to be done as a normal approximation. We note that B(200, 0.7) can be approximated by . A normal approximation is OK since 200(0.7) and 200(0.3) are both much greater than 10. Since 75% of 200 is 150, we have .

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