Math 3339 _ HOMEWORK 4 Chapter 4: Discrete Distribution For problems 1 - 4 name the type of probability distribution that can be used for each case. Show work IF POSSIBLE for full credit. 1. Of all customers purchasing automatic garage door openers, 75% purchase a chain-driven model. Let X = the number among the next 15 purcharsers who select the chain-driven model. a. Poisson b. Geometric c. Binomial d. Hypergeometric e. None of these 2. Draw marbles from a bag containing 5 red marbles, 6 bule marbles and 4 green marbles without replacement and count the number of blue marbles. a. Hypergeometric b. Geometric c. Binomial d. Poisson e. None of these 3. Draw marbles from a bag containg 5 red marbles, 6 blue marbles and 4 green marbles with replacement until you get a blue marble. a. Hypergeometric b. Geometric c. Binomial d. Poisson e. None of these 4. Draw marbles from a bag containing 5 red marbles, 6 blue marbles and 4 green marbles with replacement and count the number of blue marbles. a. Hypergeometric b. Geometric c. Binomial d. Poisson e. None of these The following table is a joint probability table for X = number of dogs a person owns and Y = number of cats a person owns. Use this to answer questions 5 - 9. 5. What is the probability P(X=0,Y =0)? a. 0.43 b. 0.35 c. 0.20 d. 0.4651 e. 0.5714 6. What is the probability that a person owns one cat, given they own one dog? a. 0.6818 b. 0.4286 c. 0.1500 d. 0.2200 e. 0.3500 7. Is \"number of dogs\" and \"number of cats\" independent? a. Yes b. No 8. How many dogs does a person expect to own? a. 1 b. 0.02 c. 0.95 d. 0.92 e. 0.35 9. Give the conditional probability distribution of number of dogs, given that they have one cat. 10. What is the total number of cats and dogs that a person is expected to own? a. 2 b. 1.87 c. 0.935 d. 1 e. None of these Use this information to answer questions 11 - 14: The number of requests for assistance received by a towing service is a Poisson process with rate of 4 per hour. 11. What is the probability that exactly ten requests are received during a particular 2-hour window? a. 0.0053 b. 0.0993 c. 0.8159 d. 0.9972 e. none of these 12. What is the probability that at most ten requests are received during a particular 2-hour window? a. 0.0053 b. 0.0993 c. 0.8159 d. 0.9972 e. none of these 13. If the operator of the towing service takes a 30-minute break for lunch, what is the probability that they do not miss any calls for assistance? a. 0.1353 b. 0.0183 c. 0.0003 d. 0.8647 e. none of these 14. How many calls would you expect during their 30-minute break? a. 4 b. 2 c. 8 d. 16 e. none of these 15. An urn contains 3 green balls, 2 blue balls, and 4 red balls. In a random sample of 5 balls, find the probability that at least one blue balls is selected. a. 1/6 b. 5/6 c. 7/9 d. 5/18 e. 5/9 For the problems 16-20, write your solution in the space provided. YOU MUST SHOW ALL WORK FOR FULL CREDIT. 16. A company that produces fine crystal knows from experience that 10% of its goblets have cosmetic flaws and must be classified as \"seconds.\"* a. Among six randomly selected goblets, how likely is it that only on is a second? b. Among six randomly selected goblets, what is the probability that at least two are seconds? c. How many out six randomly selected goblets would we expect to be seconds? d. What is the standard deviation of the number of second goblets? 17. A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite.* The geologist instructs a laboratory assistant to randomly select 15 of the specimens for analysis. a. What is the probability function of the number of granite specimens selected for analysis? b. What is the probability that all specimens of one of the two types of rock are selected for analysis? c. What is the probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value? 18. The number of requests for assistance received by a towing service is a Poisson process with average of 4 requests per hour.* a. Compute the probability that exactly ten requests are received during a particular 2-hour period. b. If the operators of the towing service take a 30-min break for lunch, what is the probability that they do not miss any calls for assistance? c. How many calls would you expect during their break? 19. A club has 50 members, 10 belonging to the ruling clique and 40 second-class members. Six members are randomly selected for free movie tickets. What is the probability that 3 or more belong to the ruling clique? 20. Huck and Jim are waiting for a raft. The number of rafts floating by over intervals of time is a Poisson process with a rate of = 0.4 rafts per day. They agree in advance to let the first raft go and take the second one that comes along. What is the probability that they will have to wait more than a week? Hint: If they have to wait more than a week, what does that say about the number of rafts in a period of 7 days? Scanned by CamScanner