Stat 207: Midterm-2 (Version A) University of Dammam Date: Saturday, May 4, 2013 Duration: 60 minutes. Instructor: Dr. Nahid Sultana Name: Student ID Number: Group: Instructions: This test consists of 23 multiple choice questions worth 1 mark each (no part marks) and 1 question worth 1 marks (no part marks) relating to the computer card. The questions must be answered on the computer card with an HB PENCIL. Marks will not be deducted for wrong answers (there is no penalty for guessing). YOU ARE RESPONSIBLE FOR ENSURING THAT YOUR COPY OF THE PAPER IS COMPLETE. BRING ANY DISCREPANCIES TO THE ATTENTION OF THE INVIGILATOR. Only standard calculator (ex. the Casio fx 991) is permitted. Computer Card Instructions: NOTE: IT IS YOUR RESPONSIBILITY TO ENSURE THAT THE ANSWER SHEET IS PROPERLY COMPLETED: YOUR EXAMINATION RESULT DEPENDS UPON PROPER ATTENTION TO THESE INSTRUCTIONS The scanner, which reads the sheets, senses the shaded areas by their non-reflection of light. A heavy mark must be made, completely filling the circular bubble, with an HB pencil. Marks made with a pen or felt-tip marker will NOT be sensed. Erasures must be thorough or the scanner may still sense a mark. Do NOT use correction fluid on the sheets. Do NOT put any unnecessary marks or writing on the sheet. Page 1
Use the following to answer question 1: Let X represent the SAT score of an entering freshman at University X. The random variable X is known to have a N(1200, 90) distribution. Let Y represent the SAT score of an entering freshman at University Y. The random variable Y is known to have a N(1215, 110) distribution. A random sample of 100 freshmen is obtained from each university. Let X = the sample mean of the 100 scores from University X, and Y = the sample mean of the 100 scores from University Y. 1. What is the probability that X will be greater than Y? A) 0.0475 B) 0.0869 C) 0.1456 D) 0.2266 2. In order to reduce the standard deviation from the sampling distribution of the sample mean, you should. A) take larger samples B) take smaller samples C) None of the above. 3. The central limit theorem says that the sampling distribution of the sample mean is approximately for large n. A) B) C) B(n,p) D) Use the following to answer question 4: The time college students spend on the internet follows a Normal distribution. At Johnson University, the mean time is 5 hrs with a standard deviation of 1.2 hrs. Page 2
4. What is the probability that the average time 100 random students on campus will spend more than 5 hours on the internet? A) 0.5 B) 1 C) 0 D) 0.2 5. The binomial distribution is a continuous distribution. A) True B) False 6. Possible values for the counts in a binomial distribution range from - to. A) True B) False 7. Probability calculations from a binomial distribution can be found using a Normal approximation for large sample sizes. A) True B) False 8. The binomial distribution can be used to model situations where there is/are outcomes. A) one B) two C) three D) four 9. One of the requirements for the binomial distribution is that the observations are all. A) independent B) random C) dependent D) continuous 10. The probability of success for binomial distribution must remain the same for each observation. A) True B) False Page 3
Use the following to answer questions 11-13: The proportion of students who own a cell phone on college campuses across the country has increased tremendously over the past few years. It is estimated that approximately 90% of students now own a cell phone. Fifteen students are to be selected at random from a large university. Assume that the proportion of students who own a cell phone at this university is the same as nationwide. Let X = the number of students in the sample of 15 who own a cell phone. 11. What is the appropriate distribution for X? A) X is N(15, 0.9) B) X is B(15, 0.9) C) X is B(15, 13.5) D) X is N(13.5, 1.16) 12. On average, how many students will own a cell phone in a simple random sample of 15 students? A) 9 B) 13 C) 13.5 D) 14 13. What is the standard deviation of the number of students who own a cell phone in a simple random sample of 15 students? A) 0.077 B) 0.09 C) 1.16 D) 1.35 Use the following to answer question 14: A comprehensive report called the Statistical Report on the Health of Canadians was produced in 1999. In it was reported that 42% of Canadians, 12 years of age or older, had their most recent eye examination within the previous year. Page 4
14. If a random sample of 20 Canadians in this age group were selected, the probability that 6, or 30%, of the selected individuals would have had their most recent eye examinations in the previous year would be: A) 20 (0.42) 6 (0.58) 14. 6 B) 20 (0.42) 14 (0.58) 6. 14 C) 12 (0.42) 6 (0.58) 6. 6 D) 20 (0.30) 6 (0.70) 14. 6 E) 20 (0.30) 14 (0.70) 6. 14 Use the following to answer question 15: In a certain game of chance, your chances of winning are 0.2. Assume outcomes are independent and that you will play the game five times. 15. What is the probability that you win at most once? A) 0.0819 B) 0.2 C) 0.4096 D) 0.7373 Use the following to answer question 16: The statistics of a particular basketball player state that he makes 4 out of 5 free-throw attempts. 16. The basketball player is just about to attempt a free throw. What do you estimate the probability that the player makes this next free throw to be? A) 0.16 B) 50-50. Either he makes it or he doesn't. C) 0.80 D) 1.2 Page 5
Use the following to answer question 17: If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. Assume the table below gives the probabilities for the color of a randomly chosen M&M: Color Brown Red Yellow Green Orange Blue Probability 0.3 0.3? 0.1 0.1 0.1 17. What is the probability that you draw neither a brown nor a green candy? A) 0.3 B) 0.6 C) 0.7 D) 0.9 18. Suppose a fair coin is flipped twice and the number of heads is counted. Which of the following is a valid probability model for the number of heads observed in two flips? A) Number of heads 0 1 2 Probability 1 4 1 2 1 4 B) C) Number of heads 0 1 2 Probability 1 4 1 4 1 4 Number of heads 0 1 2 Probability 1 3 1 2 1 3 D) None of the above. 19. Normal distributions represent random variables. A) discrete B) continuous C) None of the above. 20. A density curve describes the probability distribution of a discrete random variable. A) True B) False Page 6
Use the following to answer question 21: Consider the following probability histogram for a discrete random variable X: 21. What is P(X 3)? A) 0.10 B) 0.25 C) 0.35 D) 0.65 Use the following to answer question 22: Suppose that the random variable X is continuous and takes its values uniformly over the interval from 0 to 2. 22. What is the value of the probability P{X 0.4 or X > 1.2}? A) 0.40 B) 0.20 C) 0.60 D) 0.80 E) 0.50 Page 7
Use the following to answer question 23: A commuter must pass through five traffic lights on her way to work, and she will have to stop at each one that is red. Let X = the number of red lights she stops at on her way to work. She estimates the distribution for X to be as shown below: Value of X 1 2 3 4 5 Probability 0.40 0.25 0.15 0.15 0.05 23. On average, how many traffic lights does the commuter hit on her way to work? Include the appropriate symbol and units in your answer. A) = 2.2 lights B) = 2 lights C) x = 2.2 lights D) x = 2 lights Page 8
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Answer Key 1. C 2. A 3. A 4. A 5. B 6. B 7. A 8. B 9. A 10. A 11. B 12. C 13. C 14. A 15. D 16. C 17. B 18. A 19. B 20. B 21. D 22. C 23. A Page 16