MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS Midterm Examination Statistics 2500 - 001 Name: Winter 2003 Student No: Set by Dr. H. Wang OFFICE USE ONLY Mark: Instructions: 1. Please PRINT your name in the format of \"LAST-NAME, FIRST-NAME\". 2. This is a closed book examination. 3. You have 50 minutes to complete this exam. 4. Try to answer all questions, no penalty for guessing. 5. You may use a self-prepared formula sheet and a calculator. 6. The exam consists of 20 questions, 6 pages, and a table sheet. 7. Do NOT separate the Answer Sheet from the Exam Book. 8. Please write your answers of ALL questions on the Answer Sheet (page 2). Statistics 2500 - 001 -2- Winter 2003 Answer Sheet Circle one and only one letter below for your answers 1. N b c d e 2. a b c N e 3. a b c N e 4. a b c d N 5. a b N d e 6. a N c d e 7. N b c d e 8. a b N d e 9. a b c d N 10. a N c d e 11. N b c d e 12. a b c N e 13. a N c d e 14. a b c N e 15. N b c d e 16. a b N d e 17. a N c d e 18. a N c d e 19. a b c N e 20. N b c d e Statistics 2500 - 001 -3- Winter 2003 1. In skewed-right distributions, what is the relationship of the mean, median, and mode? (a) Mean > Median > Mode (b) Median > Mean > Mode (c) Mode > Median > Mean (d) Mode > Mean > Median (e) None of any above 2. How are x and related? (a) is the sample mean that we often use to estimate x , the population mean; (b) x and are both measures of central tendency for a data set; (c) is the population mean that we often use to estimate x , the sample mean; (d) x is the sample mean that we often use to estimate , the population mean; (e) There is no relation between x and . 3. The distribution of the amount of money spent on book purchases for a semester by MUN students has a mean of $280 and a standard deviation of $40. If the distribution is moundshaped and symmetric, what proportion of students will spend approximately between $160 and $320 this semester? (a) 0.9500 (b) 0.9750 (c) 0.8150 (d) 0.8400 (e) 1.0000 4. The average time for students in MUN to commute to the university from their home is claimed to be 20 minutes with standard deviation of 10 minutes. Assuming the elapsing time (X) for the student population is normal. If a random sample of size 4 is taken, the probability value 30} is: of P {10 X (a) 0.5639 (b) 0.9974 (c) 0.6742 (d) 0.8999 (e) 0.9544 5. The average time for students in MUN to commute to the university from their home is claimed to be 20 minutes with standard deviation of 10 minutes. Assuming the distribution of elapsing time (X) for the student population is unknown. If a random sample of size 100 is taken, the 21} is: probability value of P {19 X (a) 0.9544 (b) 0.0082 (c) 0.6826 (d) 0.9918 (e) 0.5082 Statistics 2500 - 001 -4- Winter 2003 6. The probability P {2.16 Z 0.55} of the standard normal random variable Z is: (a) 0.2758 (b) 0.6934 (c) 0.4846 (d) 0.2088 (e) 0.5154 7. The probability P {1.96 Z 0.33} of the standard normal random variable Z is: (a) 0.3457 (b) 0.4750 (c) 0.1293 (d) 0.6043 (e) 0.3707 8. What is the value of z0 for the standard normal random variable Z such that P {z0 Z < z0 } = 0.8472? (a) 1.41 (b) 1.42 (c) 1.43 (d) 1.44 (e) 1.45 9. Suppose that the random variable X N ( = 11, 2 = 4). The the probability P {10 < X 11} is: (a) 0.6915 (b) 0.3085 (c) 0.3830 (d) 0.1170 (e) 0.1915 10. Suppose that the random variable X N ( = 50, 2 = 9). What is the value of x0 for this random variable X such that P {X x0 } = 0.8413? (a) 53 (b) 47 (c) 54 (d) 45 (e) 50 11. Given the following data set {1, 4, 3, 1, 4, 4}. The numerical measurements mode, median, mean, variance and standard deviation of this data set is: (a) 4, 3.5, 2.5, 4.30, 2.07 (b) 4, 4.0, +2.5, 4.30, 2.07 (d) 4, 3.5, 2.5, 3.58, 1.89 (e) None of any above (c) +4, 4.5, 2.5, 3.58, 1.89 12. Consider the probability distribution showing here: -----------------------------------x | 1 2 4 10 -----------------------------------p(x)| 0.2 0.4 0.2 0.2 -----------------------------------What are the mean () and variance ( 2 ) of this probability distribution? (a) 3.80 & 16.25 (b) 4.25 & 16.25 (c) 4.25 & 10.56 (d) 3.80 & 10.56 (e) 3.80 & 25.00 Statistics 2500 - 001 -5- Winter 2003 13. If a data set is taken from an unknown population with mean and variance 2 , then the proportion of measurements you would expect to fall into the interval 2 is: (a) approximately 68% (b) at least 75% (c) approximately 95% (d) at least 95% (e) at least 68% 14. Let Xb be a binomial random variable with n = 200 and p = 0.06. The the mean () and standard deviation () of Xb are: (a) 12 & 11.28 (b) 6 & 3.36 (c) 6 & 11.26 (d) 12 & 3.36 (e) None of any above 15. Let Xb be a binomial random variable with n = 200 and p = 0.06. Can we use normal approximation to calculate probabilities associated with this binomial random variable Xb ? (a) Yes, since the sample size n = 200 is large enough; (b) No, since normal random variable is continuous; (c) No, since the sample size n = 200 is not large enough; (d) No, since Xb is a discrete random variable; (e) Yes, we can always use normal approximation to Xb . 16. Let Xb be a binomial random variable with n = 200 and p = 0.06. Assuming that we can use normal approximation to calculate probabilities associated with this binomial random variable Xb , then the approximated value of P {10 Xb < 20} is: (a) 0.2575 (b) 0.7647 (c) 0.7575 (d) 0.6679 (e) 0.6607 17. If events A and B are independent and P(A) = 0.6 and P(B) = 0.4, which of the following is correct? (a) P (A|B) = 0.50 (b) P (A B) = 0.76 (c) P (A B) = 1.00 (d) P (A B) = 0.24 (e) P (A B) = 0 18. What is the relationship between the events B and B c ? (a) P (B|B c ) = 1 (b) P (B|B c ) = 0 (c) P (B B c ) = 0 (d) P (B B c ) = 1 (e) P (B) = P (B c ) 19. Given two events F and G such that P (F ) = 0.40, P (G) = 0.25 and P (F |G) = 0.75. Then the value of the probability P (G F ) is: (a) 0.3375 (b) 0.1875 (c) 0.6500 (d) 0.4625 (e) 1.1500 Statistics 2500 - 001 -6- Winter 2003 20. A friend of yours claims to have the psychic gift. You are skeptical of her claim. To test her gift, you take the ace of hearts, ace of spades, ace of diamonds, and ace of clubs from a deck of cards. You randomly choose one of the cards from the deck and ask your friend (without seeing the card) to tell you what it is. You replace the card and repeat the experiment three times. If your friend is really not a psychic (and is merely guessing at the cards), what is the probability that she guesses all three cards correctly? (a) 1/64 (b) 4/64 (c) 8/64 (d) 16/64 (e) 24/64