Mat 121 Exam I Exercises Show all your work and steps to receive full credit in the exam. QUESTIONS 1. In a certain class of students, there are 11 boys from Wilmette, 4 girls from Winnetka, 7 girls from Wilmette, 4 boys from Glencoe, 5 boys from Winnetka and 4 girls from Glencoe. (a) If the teacher calls upon a student to answer a question, what is the probability that the student will be a boy? Answer: 0.571 (b) If the teacher calls upon a student to answer a question, what is the probability that the student will be from Glencoe? (c) If the teacher calls upon a student to answer a question, what is the probability that the student will be a girl given that the student is from Glencoe? (d) If the teacher calls upon a student to answer a question, what is the probability that the student will be from Glencoe given that the student is a boy? Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. 2. Assume that a study of 500 randomly selected school bus routes showed that 482 arrived on time. Is it "unusual" for a school bus to arrive late? Answer: YES 3. If a person told you in what month he was born, would it be "unusual" to guess the date of his birth (not including the year)? Answer: YES 4. A study conducted at a certain college shows that 65% of the school's graduates nd a job in their chosen eld within a year after graduation. Find the probability that 11 randomly selected graduates all nd jobs in their chosen eld within a year of graduating. Round to the nearest thousandth if necessary. Answer: 0.009 Page 1 of 4 5. Evaluate the followings (a) 10!, 4!, 5!, 7! (b) 9 C 5 , 11 C 6 , 12 C 7 (c) 9 P5 , 11 P6 , 12 P7 6. If a person is randomly selected, nd the probability that his or her birthday is not in May. Ignore leap years. Answer: 334 365 7. In one town, 66% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance? Round to the nearest thousandth if necessary Answer: 0.19 8. A die is rolled 9 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, nd the mean for the number of two's. Answer: 1.5 9. A tennis player makes a successful rst serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 rst serves in? Assume that each serve is independent of the others. Answer: 0.154 10. A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 634 consumers who recognize the Dull Computer Company name? Answer: YES 11. In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority? Answer: 0.982 12. A company manufactures batteries in batches of 6 and there is a 3% rate of defects. Find the mean number of defects per batch. Answer: 0.2 Page 2 of 4 13. A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? Answer: 0.377 14. A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will fail the test? Answer: 1-0.377 15. Find the mean of the given probability distribution. Answer: 1.60 16. A contractor is considering a sale that promises a prot of $38,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $16,000 with a probability of 0.3. What is the expected prot? Answer: $21,800 17. Find the probability of x successes in n trials given the probability p of success on a single trial. n = 12, x = 5, p = 0.25 Answer: 0.103 Page 3 of 4 18. Determine if the following is a probability distribution. Answer: No 19. A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? Answer: 3/16 20. Assume that one student in a class of 27 students is randomly selected to win a prize. Would it be \"unusual\" for you to win? (Assume \"unusual\" is a probability less than or equal to 0.05) Answer: Yes 21. A bag contains 8 red marbles, 4 blue marbles, and 1 green marble. Find P(not blue). Answer: 9/13 22. A company manufactures glass bottles. The probability that a randomly selected bottle is defective is 0.002. What is the probability that a randomly selected bottle is not defective? Answer: .998 Page 4 of 4