Binomial Distributions, Geometric Distributions, and Sampling Distributions Multiple Choice Practice Problems for AP Statistics

Review the following concepts if necessary:

• Binomial Distributions for AP Statistics
• Normal Approximation to the Binomial for AP Statistics
• Geometric Distributions for AP Statistics
• Sampling Distributions for AP Statistics
• Sampling Distributions of a Sample Proportion for AP Statistics

Problems

1. A binomial event has n = 60 trials. The probability of success on each trial is 0.4. Let X be the count of successes of the event during the 60 trials. What are μ_x and σ_x?
   1. 24, 3.79
   2. 24, 14.4
   3. 4.90, 3.79
   4. 4.90, 14.4
   5. 2.4, 3.79
2. Consider repeated trials of a binomial random variable. Suppose the probability of the first success occurring on the second trial is 0.25. What is the probability of success on the first trial?
   1. 1/4
   2. 1
   3. 1/2
   4. 1/8
   5. 3/16
3. To use a normal approximation to the binomial, which of the following does not have to be true?
   1. np ≥ 5, n(1 –p)≥ 5 (or: np ≥ 10, n (1–p) ≥10).
   2. The individual trials must be independent.
   3. The sample size in the problem must be too large to permit doing the problem on a calculator.
   4. For the binomial, the population size must be at least 10 times as large as the sample size.
   5. All of the above are true.
4. You form a distribution of the means of all samples of size 9 drawn from an infinite population that is skewed to the left (like the scores on an easy Stats quiz!). The population from which the samples are drawn has a mean of 50 and a standard deviation of 12. Which one of the following statements is true of this distribution?
   1. the sampling distribution is skewed somewhat to the left.
   2. the sampling distribution is skewed somewhat to the left.
   3. the sampling distribution is approximately normal.
   4. the sampling distribution is approximately normal.
   5. the sample size is too small to make any statements about the shape of the sampling distribution.
5. A 12-sided die has faces numbered from 1–12. Assuming the die is fair (that is, each face is equally likely to appear each time), which of the following would give the exact probability of getting at least 10 3s out of 50 rolls?



6. In a large population, 55% of the people get a physical examination at least once every two years. An SRS of 100 people are interviewed and the sample proportion is computed. The mean and standard deviation of the sampling distribution of the sample proportion are
   1. 55, 4.97
   2. 0.55, 0.002
   3. 55, 2
   4. 0.55, 0.0497
   5. The standard deviation cannot be determined from the given information.
7. Which of the following best describes the sampling distribution of a sample mean?
   1. It is the distribution of all possible sample means of a given size.
   2. It is the particular distribution in which μ = μ and σ = σ.
   3. It is a graphical representation of the means of all possible samples.
   4. It is the distribution of all possible sample means from a given population.
   5. It is the probability distribution for each possible sample size.
8. Which of the following is not a common characteristic of binomial and geometric experiments?
   1. There are exactly two possible outcomes: success or failure.
   2. There is a random variable X that counts the number of successes.
   3. Each trial is independent (knowledge about what has happened on previous trials gives you no information about the current trial).
   4. The probability of success stays the same from trial to trial.
   5. P(success) + P(failure) = 1.
9. A school survey of students concerning which band to hire for the next school dance shows 70% of students in favor of hiring The Greasy Slugs. What is the approximate probability that, in a random sample of 200 students, at least 150 will favor hiring The Greasy Slugs?