Chapter 5 QUESTIONS and ANSWERS

1. The binomial experiment consists of n independent, identical trials, each of which results in either success or failure and is such that the probability of success on any trial is the same. True False 2. A Poisson random variable is a continuous variable that can be used to describe the number of occurrences of an event over a specified interval of time or space. True False 3. A discrete random variable may assume a countable number of outcome values. True False 4. The variable "home ownership" can take on one of two values, 1 if the person living in a home owns the home and zero if the person living in a home does not own the home is an example of a discrete random variable. True False 5. If the number of surface nonconformities on a specific size of a metal piece is the discrete random variable in question, then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 nonconformities is most likely given by the binomial distribution. True False 6. The mean of the binomial distribution is np(1-p). True False 7. In a binomial experiment, the results of one trial are dependent on the results of other trials. True False 8. In a binomial distribution the random variable X is continuous. True False 9. Your company's internal auditor believes that 10% of the company's invoices contain errors. To check this theory, 20 invoices are randomly selected and 5 are found to have errors. The auditor's claim will be rejected. True False 10. The mean and the variance of a Poisson random variable are equal. True False 11. Depending on the mean of the Poisson distribution, the distribution can either be very skewed to the right or quite symmetrical. True False 12. For a discrete probability distribution, the value of p(x) for each value of x falls between -1 and 1. True False 13. The expected value of the discrete random variable x is the population mean. True False 14. The standard deviation of a discrete random variable measure the spread of the population of all possible values of x. True False 15. The time (in seconds) it takes for an athlete to run 50 meters is an example of a continuous random variable. True False 16. Hypergeometric probability distribution can be approximated by the Poisson distribution. True False 17. If the population size is at least 20 times larger than the sample size, a hypergeometric distribution can be approximated by the binomial distribution. True False 18. In a hypergeometric probability distribution of a population of N items, r refers to the number of successes and N-r the number of failures. True False 19. The random variable x has a hypergeometric distribution and the population contains 12 items. If you wanted to find the number of defects in a random sample of 3 selected items when the population contains 5 defects, identify the N, n and r. A. N = 3, n = 12, r = 5 B. N = 5, n = 12, r = 7 C. N = 12, n = 5. r = 3 D. N = 12, n = 3, r = 5 20. A hypergeometric random variable x has a distribution that is approximated by a binomial distribution when: A. Number of successes is larger than number of failures in the population B. Sample is selected from population without replacement C. Population is much larger than the sample size D. Sample size is half the size of the original population 21. In the context of the hypergeometric distribution, r is A. Sample size B. Number of items in the population that are successes C. Number of times items are sampled without replacement D. Number of items in the sample that are successes 22. Which of the following is not a discrete random variable? A. The number of times a light changes red in a 10 minute cycle. B. The number of minutes required to run 1 mile. C. The number of defects in a sample selected from a population of 100 products. D. The number of criminals found in a five mile radius of a neighborhood. 23. A random variable: A. Is the result of a measurement B. Can only be discrete C. Can be thought of as representing an uncertain numerical outcome to an experiment D. Is either a binomial, poisson or hypergeometric variable 24. A probability distribution of a discrete random variable is expressed as a table, graph or _____. A. Binomial B. Formula C. Poisson D. Hypergeometric