Chapter 6

4. In which of the following distributions is the probability of a success usually small? A. Binomial B. Poisson C. Hypergeometric D. All distribution

The correct answer is b. That's why it is often referred to as the "law of improbable events."

10. The expected value of the a probability distribution A. Is the same as the random variable. B. Is another term for the mean. C. Is also called the variance. D. Cannot be greater than 1.

The correct answer is b. The average or mean describes what you "expect."

3. The mean and the variance are equal in A. All probability distributions. B. The binomial distribution. C. The Poisson distribution. D. The hypergeometric distribution.

The correct answer is c. The mean and variance of the binomial are nπ and nπ(1-π), respectively.

2. Which of the following is not a requirement of a binomial distribution? A. A constant probability of success. B. Only two possible outcomes. C. A fixed number of trails. D. Equally likely outcomes.

The correct answer is d. A binomial distribution has only two possible outcomes on each trial, results from counting successes over a series of trials, the probability of success stays the same from trial to trial and successive trials are independent.

6. For a binomial distribution A. n must assume a number between 1 and 20 or 25. B. must be a multiple of .10. C. There must be at least 3 possible outcomes. D. None of the above.

The correct answer is d. A binomial distribution has only two possible outcomes on each trial, results from counting successes over a series of trials, the probability of success stays the same from trial to trial and successive trials are independent.

1. The difference between a random variable and a probability distribution is A. A random variable does not include the probability of an event. B. A random variable can only assume whole numbers. C. A probability distribution can only assume whole numbers. D. None of the above.

The correct answer is a. A random variable is a value resulting from an experiment, while a probability distribution is a listing of all possible outcomes and their associated probability.

9. For a binomial distribution with n = 15 as changes from .50 toward .05 the distribution will A. Become more positively skewed. B. Become more negatively skewed C. Become symmetrical. D. All of the above.

The correct answer is a. As the likelihood of success gets smaller, the positive tail gets relatively longer.

5. Which of the following is not a requirement of a probability distribution? A. Equally likely probability of a success. B. Sum of the possible outcomes is 1.00. C. The outcomes are mutually exclusive. D. The probability of each outcome is between 0 and 1.

The correct answer is a. Only the classical notion of probability requires the events to be equally likely.

7. Which of the following is a major difference between the binomial and the hypergeometric distributions? A. The sum of the outcomes can be greater than 1 for the hypergeometric. B. The probability of a success changes from trial to trial in the hypergeometric distribution. C. The number of trials changes in the hypergeometric distribution. D. The outcomes cannot be whole numbers in the hypergeometric distribution.

The correct answer is b. A typical case where the hypergeometric distribution applies is sampling without replacement. Hence the probability of a success changes from trial to trial.

8. In a continuous probability distribution A. Only certain outcomes are possible. B. All the values within a certain range are possible. C. The sum of the outcomes is greater than 1.00 D. None of the above.

The correct answer is b. Continuous implies without interruption. So it includes all numbers, without exception, in a range.