Chapter 8 Practice Quiz.YMS Name: __________________________ Date: _____________ 1. An airplane has a front door and a rear door that are both opened to allow passengers to exit when the plane lands. The plane has 100 passengers seated. The number of passengers exiting through the front door should have A) a binomial distribution with mean 50. B) a binomial distribution with 100 trials but success probability not equal to 0.5. C) a binomial distribution with 50 trials but success probability not equal to 0.5. D) a normal distribution with a standard deviation of 5. E) none of the above distributions. 2. A set of 10 cards consists of five red cards and five black cards. The cards are shuffled thoroughly and I choose six of them at random. Let X be the number of red cards observed in the six chosen. The random variable X has which of the following probability distributions? A) The normal distribution with mean 3 and variance 1.22. B) The binomial distribution with parameters n = 6 and p = 0.5. C) A skewed right distribution. D) The uniform distribution on 0, 1, 2, 3, 4, 5, and 6. E) None of the above. 3. If X is binomial with parameters n = 9 and p = 1/3, the standard deviation σX of X is A) 6. B) 3. C) 2. D) 1.414. E) 1.732. 4. In a certain game of chance, your chances of winning are 0.2. You play the game five times and outcomes are independent. Suppose it costs $1 to play the game each time. Each time you win, you receive $4 (for a net gain of $3). Each time you lose, you receive nothing (for a net loss of $1). Your expected winnings for five plays are A) $3. B) $1. C) $0. D) –$1. E) –$2. Use the following to answer question 5: A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let X denote the number in the sample that say they support the increase. Suppose that 40% of all adults in Ohio support the increase. 5. The probability that X is more than 750 is A) less than 0.0001. B) about 0.1. C) 0.3372. Page 1 D) 0.4602. E) 0.5. Chapter 8 Practice Quiz.YMS 6. A fair coin (one for which both the probability of heads and the probability of tails are 0.5) is tossed 60 times. The probability that less than 1/3 of the tosses are heads is A) 0.33. B) 0.109. C) 0.09. D) 0.034. E) 0.005. 7. A multiple-choice exam has 100 questions, each with five possible answers. If a student is just guessing at all the answers, the probability that he or she gets more than 30 correct is A) 0.3100. B) 0.2000. C) 0.1587. D) 0.1020. E) 0.0062. 8. A college basketball player makes 5/6 of his free throws. Assuming free throw attempts are independent, the probability that he makes exactly three of his next four free throws is 3 1 A) 1 5 4    . 6 6 B) 1 5    . 6 6 C) 1 5 3    . 6 6 3 1 1 5     . 6 6 E) 1 5 4    . 6 6 1 1 3 D) 1 3 3 9. Which of the following random variables is geometric? A) The number of phone calls received in a one-hour period. B) The number of cards I need to deal from a deck of 52 cards that has been thoroughly shuffled so that at least one of the cards is a heart. C) The number of digits I will read beginning at a randomly selected starting point in a table of random digits until I find a 7. D) The length of time a traffic light must be green so that 5 cars can make a left turn. E) All of the above. 10. In a test of ESP (extrasensory perception), the experimenter looks at cards that are hidden from the subject. Each card contains a star, a circle, a wavy line, or a square. The subject tries to read the experimenter's mind and name the shape on each card. What is the probability that the subject gets the first four correct before giving a wrong answer if he is just guessing? A) 0.00293. B) 0.00391. C) 0.06328. D) 0.07910. E) 0.31641. Page 2 Chapter 8 Practice Quiz.YMS 11. A college basketball player makes 80% of her free throws. Suppose this probability is the same for each free throw she attempts, and free throw attempts are independent. The probability that it takes more than three free throws before she makes her first free throw A) is 0.512. B) is 0.032. C) is 0.008. D) is 0.006. E) cannot be determined from the information given. 12. A small class has 10 students. Five of the students are male and five are female. I write the name of each student on a 3-by-5 card. The cards are shuffled thoroughly and I choose one at random, observe the name of the student, and replace it in the set. The cards are thoroughly reshuffled and I again choose a card at random, observe the name, and replace it in the set. Let X be the number of cards observed until I get one with a name corresponding to a male student. The probability that X is greater than 1 is A) 0.125. B) 0.200. C) 0.250. D) 0.500. E) 0.750. 13. A small class has 10 students. Five of the students are male and five are female. I write the name of each student on a 3-by-5 card. The cards are shuffled thoroughly and I choose one at random, observe the name of the student, and replace it in the set. The cards are thoroughly reshuffled and I again choose a card at random, observe the name, and replace it in the set. Let X be the number of cards observed until I get one with a name corresponding to a male student. The random variable X has which of the following probability distributions? A) A normal distribution with mean 0.5. B) The geometric distribution with probability of success 0.1. C) A uniform distribution. D) The geometric distribution with probability of success 0.5. E) A binomial distribution with p = 0.5. 14. A fair coin (one for which both the probability of heads and the probability of tails are 0.5) is tossed six times. The probability that less than 1/3 of the tosses are heads is A) 0.33. B) 0.2061. C) 0.109. D) 0.09. E) 0.0043. 15. In a certain game of chance, your chances of winning are 0.2. If you play the game five times and outcomes are independent, the probability that you win all five times is A) 1. B) 0.6723. C) 0.3277. D) 0.04. E) 0.00032. Page 3 Chapter 8 Practice Quiz.YMS Answer Key 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. E E D D A E E E C A C D D C E Page 4