2377 Practise Final

MAT 2377 Final Examination Winter 2020 Final Exam Version: 27866 April 20, 2020 Time Limit: 3 Hours Start Time: 2PM EST This exam contains 37 pages (including this cover page and tables) and 110 questions. Read carefully: if you submit answers for this online examination, you promise and certify that all work done during the assigned exam period will be done entirely by yourself, with no help from others; you will not communicate with anybody except the professor during the exam, for exam- and course-related questions; you will not consult any people, sources, or writings other than the course textbook, your self-made review sheets, your course notes, your prepared answers, the course documents made available on Brightspace, and the exam itself; you will not provide information related to the exam’s contents to other people until 24 hours after the exam is over. Obviously, we do not have a way to monitor your adherence to these instructions (nor do we really wish to look for one); we will be asking, instead, for your word of honour that you will follow the directives and work on this examination alone. Multiple choice questions and true or false question are worth 1 mark each; short answer questions, 2 marks. There are no part marks. For each question, record your answer in the corresponding space on the answer sheet that has been provided separately (save your file regularly). For multiple choice questions, select the closest answer among the options, when appropriate; for short answer questions, provide an answer to at least 2 decimals. IMPORTANT: every student has been assigned a different exam (based on the last 5 digits of your student number). You need to answer the questions of the final exam that has been specifically assigned to you. When you have answered all the questions and you are ready to upload the answers to Brightspace, save your answers to the file Answer_Sheet_27866.pdf . We suggest that you print and scan or take a screenshot (with time stamp) of your completed answer sheet before uploading to Brightspace (see the appropriate location in the “Assignment” section where you uploaded your 3rd assignment), and that you keep a copy of these documents (with time stamp). Should Brightspace’s upload functionality does not work when you are ready to submit, wait a little bit and try again; as a last recourse, please email your answer sheet with saved answers to pboily@uottawa.ca if you are registered in section A or iyadegar@uottawa.ca if you are registered in section B. No worries. You’ve got this. MAT 2377 Final Exam - Page 2 of 37 April 20, 2020 1. [1] Multiple Choice Question An insurance company divides its customers into three classes: with low risk, medium risk and high risk. For each group, the probability that a person has at least one accident within a year is, respectively, 0.05, 0.15 and 0.25. It is estimated that 50% of the population is in low risk group, 35% in medium risk group, and 15% in the high risk group. One person is selected at random. What is the probability that this person will have at least one accident within a year? A. 0.215 B. 0.115 C. 0.45 D. 0.095 E. none of the preceding 2. [1] Multiple Choice Question From a group of 25 members of a Board of Directors, in how many ways one can select a vice-president and a president? (vice-president and president are different persons). A. 25 B. 50 C. 600 D. 625 E. none of the preceding 3. [1] Multiple Choice Question In how many ways can we select four out of 12 companies renting construction equipment to be ranked as first, second, third and fourth? A. 11880 B. 20736 C. 495 D. 12 E. none of the preceding 4. [1] Multiple Choice Question In a pile of 20 tires, three of them are defective. Four tires are selected randomly for inspection. What is the probability that exactly one is defective? A. 0.15 B. 0.42 C. 0.1053 D. 0.4912 E. none of the preceding 5. [1] Multiple Choice Question A company has four technicians. The technicians T1, T2, T3 and T4 repair 20%, 15%, 50% and 15% of failures, respectively. Suppose that these technicians do not complete their repairs in 3%, 1%, 2% and 1% cases, respectively. If a repair has not been completed, what is the probability that this job was conducted by technician T1? A. 0.019 B. 0.05 C. 0.316 D. 0.20 E. none of the preceding

MAT 2377 Final Exam - Page 3 of 37 April 20, 2020 6. [1] Multiple Choice Question Consider the following system with six components. It operates only if there is a path of functional components from left to the right. The probability that each components functions is as shown. What is the probability that the circuit operates? Assume independence. A. 0.723 B. 0.373 C. 0.511 D. 0.633 E. none of the preceding 7. [1] Multiple Choice Question Consider the following system with four components. It operates only if there is a path of functional components from left to the right. The probability that each component functions is as shown. What is the probability that the circuit operates? Assume independence. A. 0.32 B. 0.16 C. 0.035 D. 0.68 E. none of the preceding 8. [1] Multiple Choice Question A group of 20 workers was surveyed to obtain their opinion about new security measures. If 12 workers are in favour of the new rules and 8 oppose them, what is the probability that two randomly selected workers (from the group of twenty) oppose the new security measures? A. 2/44 B. 14/95 C. 1/6 D. 12/45 E. none of the preceding MAT 2377 Final Exam - Page 4 of 37 April 20, 2020 9. [1] Multiple Choice Question Consider the following system with five components. It operates only if there is a path of functional components from left to the right. The probability that each device functions is as shown. What is the probability that the circuit operates? Assume independence. A. 0.84 B. 0.16 C. 0.035 D. 0.50 E. none of the preceding 10. [1] Multiple Choice Question In a study on opposite-sex couples and work, 1000 couples have both the male and the female working. Each person was asked whether his or her salary exceeded $30,000. The following information was obtained. M ≤ $30 K M > $30 K F ≤ $30 K 430 410 F > $30 K 60 100 What is the probability that a female earns more than $30K given that the male earns less than $30K? A. 0.8059 B. 0.1961 C. 0.1224 D. 0.5700 E. none of the preceding 11. [1] Multiple Choice Question Consider a box of 50 fuses which contains 8 faulty fuses. Five fuses are selected at random. What is the probability that none of them is faulty? A. 0.4015 B. 0.84 C. 0.3725 D. 0.4275 E. none of the preceding 12. [1] Multiple Choice Question Fifteen individuals volunteered to take part in an experiment. We have 5 treatments. We want to partition the 15 subjects into 5 treatment groups of equal size. In how many different ways can we accomplish this task? A. 1024 B. 325 C. 15 D. 168,168,000 E. none of the preceding

MAT 2377 Final Exam - Page 7 of 37 April 20, 2020 24. [1] Multiple Choice Question The lifetime of a voltage regulator for a car follows an exponential distrubution with a mean of 6 years. The number of failures follows a Poisson distribution with a mean of one failure every 6 years. A person buys a 6-year-old car and counts on owning it for another 6 years. If the regulator suffers a failure 3 years after the purchase, compute the average number of years until the next failure. A. 6 B. 0 C. 3 D. 12 E. none of the preceding 25. [1] Multiple Choice Question The air pressure in a random tire on a certain new car model is normally distributed with a mean of 31lb/in 2 and a standard deviation of 0.5lb/in 2 . What is the probability that the pressure of a randomly selected tire falls between 30.5 and 31.5 lb/in 2 ? A. 0.6827 B. 0.3173 C. 0.5000 D. 0.4245 E. none of the preceding 26. [1] Multiple Choice Question Trucks arrive at a loading/unloading station according to a Poisson process with a rate of 2 trucks per hour. Determine the probability that at least 3 trucks will arrive at the station in the next 30 minutes. A. 0.86 B. 0.59 C. 0.13 D. 0.81 E. 0.08 27. [1] Multiple Choice Question Trucks arrive at a loading/unloading station according to a Poisson process with a rate of 2 trucks per hour. A truck just arrived at the station. A station employee would like to know if he has enough time to take a break. Let the random variable T represent the waiting time (in hours) until the next truck arrival. What is the probability that the employee has 15 minutes until the next arrival (that is, determine P ( T > 0 . 25))? A. 0.5 B. 0.3435 C. 0.6065 D. 0.7788 E. none of the above 28. [1] Multiple Choice Question In a nickel-cadmium battery NiCd, a fully charged cell consists of nickelic hydroxide. Nickel is an element which has multiple oxidation states. Let X be the charge of nickel, which has the following probability mass function: x f X ( x ) 0 0 . 18 1 0 . 34 2 0 . 33 4 0 . 15 Determine the mean charge of nickel. A. 2.0 B. 1.5 C. 1.6 D. 1.45 E. none of the preceding MAT 2377 Final Exam - Page 8 of 37 April 20, 2020 29. [1] Multiple Choice Question Let X be the number of failures for a certain machine during a month. Its cumulative distribution function is F X ( x ) =                          0 if x < 0 0 . 17 if 0 ≤ x < 1 0 . 40 if 1 ≤ x < 2 0 . 59 if 2 ≤ x < 3 0 . 72 if 3 ≤ x < 4 0 . 80 if 4 ≤ x < 5 1 if x ≥ 5 Compute the probability that there will be more than 3 failures during a month. A. 0.28 B. 0.72 C. 0.20 D. 0.80 E. 0.41 30. [1] Multiple Choice Question Let X be the number of failures for a certain machine during a month. Its cumulative distribution function is F X ( x ) =                          0 if x < 0 0 . 17 if 0 ≤ x < 1 0 . 40 if 1 ≤ x < 2 0 . 59 if 2 ≤ x < 3 0 . 72 if 3 ≤ x < 4 0 . 80 if 4 ≤ x < 5 1 if x ≥ 5 What is the expected number of failures for a month? A. 2.50 B. 3.00 C. 2.32 D. 11.94 E. none of the above 31. [1] Multiple Choice Question Suppose that 10% of the chips produced by a computer hardware factory are defec- tive. If you order 5 chips, what is the probability of receiving at most one defective chip? A. 0.9000 B. 0.6561 C. 0.9185 D. 0.3280 E. none of the above 32. [1] Multiple Choice Question The lifetime (in 1,000 km) for a certain brand of tire is modeled as a continuous random variable with the following cumulative distribution function: F ( x ) = 1 - e - ( x - 10) / 50 , x > 10. Determine a lifetime x (in 1,000 km) that will be exceeded by 60% of the tires. A. 44.66 B. 50 C. 55.81 D. 35.54 E. none of the above

MAT 2377 Final Exam - Page 9 of 37 April 20, 2020 33. [1] Multiple Choice Question Suppose that the number of bad cheques received by a bank in one day is a Poisson random variable with mean λ = 3. Determine the probability that the bank will receive 4 bad cheques in 2 days. A. 0.134 B. 0.058 C. 0.316 D. 0.205 E. none of the above 34. [1] Multiple Choice Question Suppose the reaction time at a traffic light that a driver takes to brake is normally distributed with mean μ = 1 . 25 seconds and standard deviation σ = 0 . 2 seconds. What is the probability that the time to react to a red traffic light will be larger than 1.75 seconds? A. 0.1054 B. 0.2397 C. 0.3456 D. 0.0062 E. 0.0538 35. [1] Multiple Choice Question The time (in days) that a surveillance camera will be used is a continuous random variable X with probability density function f ( x ) = (10 - x ) / 50, for 0 ≤ x ≤ 10. What is E[ X ]? A. 10/3 B. 5 C. 75/3 D. 10 E. none of the preceding 36. [1] Multiple Choice Question Let X be a random variable with the following cumulative distribution function: F ( x ) =      0 x ≤ - 1 0 . 75 x - 0 . 25 x 3 + 0 . 5 - 1 ≤ x ≤ 1 1 x ≥ 1 Compute the mean and the variance of X . A. 0 and 3 B. 1 and 0.2 C. 1 and 3 D. 0 and 0.2 E. none of the preceding 37. [1] Multiple Choice Question The cross section of a plastic tube for use in pulmonary resuscitators is normally distributed with a mean of 12.5mm 2 and a standard deviation of 0.2 mm 2 . When the cross section is less than 12mm 2 or more than 13 mm 2 , the tube will not be adjusted properly. What is the probability that a randomly selected tube will be adjusted properly? A. 0.9538 B. 0.9998 C. 0.9890 D. 0.9745 E. 0.9876 MAT 2377 Final Exam - Page 10 of 37 April 20, 2020 38. [1] Multiple Choice Question Consider the discrete random variables X and Y with the following joint probability mass function: x y f XY ( x, y ) - 1 0 1 / 8 0 - 1 1 / 4 0 1 1 / 4 1 0 1 / 8 - 1 1 1 / 8 1 - 1 1 / 8 Compute the covariance Cov( X, Y ) = E[ XY ] - E[ X ]E[ Y ]. A. 7/8 B. 3/8 C. 1/4 D. -1/4 E. none of the preceding 39. [1] Multiple Choice Question Consider the discrete random variables X and Y with the following joint probability mass function: x y f XY ( x, y ) - 1 0 1 / 8 0 - 1 1 / 4 0 1 1 / 4 1 0 1 / 8 - 1 1 1 / 8 1 - 1 1 / 8 Given that X is not negative, what is the probability that Y is also not negative? A. 0.5 B. 0.8 C. 0.4 D. 0.25 E. none of the preceding 40. [1] Multiple Choice Question Consider the discrete random variables X and Y with the following joint probability mass function: x y f XY ( x, y ) - 1 0 1 / 8 0 - 1 1 / 4 0 1 1 / 4 1 0 1 / 8 - 1 1 1 / 8 1 - 1 1 / 8 What are the mean and the variance of X ? A. 0; 0.25 B. 0; 0.5 C. 0.1; 0.5 D. 0.5; 0.5 E. none of the preceding

MAT 2377 Final Exam - Page 13 of 37 April 20, 2020 50. [1] Multiple Choice Question A company produces photocopiers. The mean lifetime of a photocopier is 6 years and the standard deviation of the lifetime is 2.5 years. Consider a random sample of 50 photocopiers. Approximate the probability that the mean lifetime of these 50 photocopiers will exceed 7 years. A. 0.0023 B. 0.9977 C. 0.6554 D. 0.3446 E. none of the preceding 51. [1] Multiple Choice Question Consider two independent populations with the following means and variances: μ 1 , μ 2 , σ 2 1 , σ 2 2 . To estimate the difference θ = μ 1 - μ 2 , we use ˆ Θ = X - Y , where X and Y are the sample means from the respective populations, based on samples of sizes n 1 , n 2 , respectively. Which of the following statements is true? A. E[ ˆ Θ] = θ and Var[ ˆ Θ] = σ 2 1 /n 1 + σ 2 2 /n 2 B. E[ ˆ Θ] 6 = θ and Var[ ˆ Θ] = σ 2 1 /n 1 + σ 2 2 /n 2 C. E[ ˆ Θ] = θ and Var[ ˆ Θ] = σ 2 1 /n 1 - σ 2 2 /n 2 D. E[ ˆ Θ] 6 = θ and Var[ ˆ Θ] = σ 2 1 /n 1 - σ 2 2 /n 2 E. none of the preceding 52. [1] Multiple Choice Question The service time at a customer service counter has a mean of 176 seconds with a variance of 400. A random sample of 100 clients is selected. What is the approximate probability that the sample mean will fall between 175 and 177 seconds? A. 0.691 B. 0.383 C. 0.277 D. 0.288 E. none of the preceding 53. [1] Multiple Choice Question Assume that the yearly rainfall in Winnipeg is normally distributed with mean 35.4 inches and standard deviation 4.2 inches. A university student is in Winnipeg for 4 years. Assume that yearly rainfall are independent. Let D = X 1 - X 4 be the difference of the rainfall in year 1 and in year 4. Compute the mean and the standard deviation of D , respectively. A. 0; 8.4 B. 0; 5.9 C. 0; 0 D. -35.4; 5.9 E. -35.4; 8.4 MAT 2377 Final Exam - Page 14 of 37 April 20, 2020 54. [1] Multiple Choice Question A sample of 20 fish are captured in lake A and their concentrations of polychlorinated biphenyl are measured using a certain technique. Furthermore, 15 fish are captured in lake B and and their concentrations of polychlorinated biphenyl are measured. The data (in parts per million) are summarized as follows: Lake A Lake B mean 12.42 12.50 standard deviation 1.167 1.141 sample size 20 15 Boxplots are constructed for each lake: Is it reasonable to assume that A. the populations are normal with equal variances B. the populations are normal with unequal variances C. only one of the populations is normal D. the populations are not normal E. none of the preceding

MAT 2377 Final Exam - Page 15 of 37 April 20, 2020 55. [1] Multiple Choice Question Suppose that we want to compare the waiting times between repairs of two systems (in days), S 1 and S 2 . Here are histograms of the waiting times: Is it reasonable to assume that A. the populations are normal with equal variances B. the populations are normal with unequal variances C. the populations are not normal D. only one of the populations is normal E. none of the preceding MAT 2377 Final Exam - Page 16 of 37 April 20, 2020 56. [1] Multiple Choice Question Consider the following boxplots: It appears that the disperson of A. the first sample is the largest B. the second sample is the largest C. the first and second sample is the same D. both samples cannot be compared E. none of the preceding 57. [1] Multiple Choice Question Consider the following random sample: 16, 13, 10, 17, 16, 14, 5, 12, 15, 8. Calculate the first quartile (choose the best answer). A. 9.5 B. 7.5 C. 10.5 D. 0.25 E. 11 58. [1] Multiple Choice Question Consider the following sample: 16, 13, 10, 17, 16, 14, 5, 12, 15, 8, 9, 10, 15, 22, 8. Calculate the mean and median of the sample, respectively. A. 11.67; 12.5 B. 190.0; 13 C. 12.667; 12.5 D. 12.667; 13 E. none of the preceding 59. [1] Multiple Choice Question Consider the following sample: 16, 13, 10, 17, 16, 14, 5, 12, 15, 8, 9, 10, 15, 22, 8. Calculate the variance and interquartile range of the sample, respectively. A. 19.38; 7 B. 15.7; 7 C. 4.40; 7 D. 19.38; 7.5 E. 19.38; 6.5 60. [1] Multiple Choice Question Consider the following random sample: 5, 34, 12, 10, 4. Calculate the mean and variance of the sample, respectively. A. 13; 149 B. 13; 119.2 C. 12; 119.2 D. 13; 12.2 E. none of the preceding

MAT 2377 Final Exam - Page 19 of 37 April 20, 2020 71. [1] Multiple Choice Question Previous experience has shown that the breaking strength of the fabric used in a certain brand of drapes is normally distributed with a standard deviation of 2 pounds per square inch. A random sample of 9 specimens is examined to reveal an average breaking strength of x = 98 pounds per square inch. Determine the p - value required to test the hypothesis that the true mean exceeds 97. A. 0.067 B. 0.012 C. 0.13 D. 0.006 E. none of the preceding 72. [1] Multiple Choice Question Previous experience has shown that the breaking strength of the fabric used in a certain brand of drapes is normally distributed with a standard deviation of 2 pounds per square inch. A random sample of 9 specimens is examined to reveal an average breaking strength of x = 98 pounds per square inch. Determine the p - value required to test the hypothesis that the true mean is not 97. A. 0.067 B. 0.012 C. 0.13 D. 0.006 E. none of the preceding 73. [1] Multiple Choice Question Previous experience has shown that the breaking strength of the fabric used in a certain brand of drapes is normally distributed with a standard deviation of 2 pounds per square inch. A random sample of 25 specimens is examined to reveal an average breaking strength of x = 98 pounds per square inch. Determine the p - value required to test the hypothesis that the true mean is not 97. A. 0.067 B. 0.012 C. 0.13 D. 0.006 E. none of the preceding 74. [1] Multiple Choice Question Previous experience has shown that the breaking strength of the fabric used in a certain brand of drapes is normally distributed with with a mean of 97 pounds per square inch. A random sample of 9 specimens is examined to reveal an average breaking strength of x = 98 pounds per square inch and a standard deviation of 2 pounds per square inch are observed. The p - value to test the hypothesis that the true mean is not 97 is between A. (0.05,0.1) B. (0.1,0.2) C. (0.025,0.05) D. [0,0.025) E. none of the preceding 75. [1] Multiple Choice Question A new treatment has been developed for a certain type of cement, resulting in a mean pressure resistance of 5000kg/cm 2 and a standard deviation of 130kg/cm 2 . To verify the null hypothesis of μ = 5000 against the alternative of μ < 5000, a random sample of 50 pieces of cement are examined. Determine the probability of committing a Type II error if μ = 4960 and α = 0 . 05. A. 0.298 B. 0.954 C. 0.082 D. 0.105 E. none of the preceding MAT 2377 Final Exam - Page 20 of 37 April 20, 2020 76. [1] Multiple Choice Question An engineer measures the weights (in kilograms) of steel pieces. They would like to test H 0 : μ = 5 against H 1 : μ > 5. The weights follow a normal distribution with variance 16. Using a sample of size n = 25, the engineer decides to reject H 0 if x > 6. Determine the probability of committing an error of Type I error. A. 0.0500 B. 0.1057 C. 0.8943 D. 0.1000 E. none of the preceding 77. [1] Multiple Choice Question An engineer measures the weights (in kilograms) of steel pieces. They would like to test H 0 : μ = 5 against H 1 : μ > 5. The weights follow a normal distribution with variance 16. Using a sample of size n = 25, the engineer decides to reject H 0 if x > 6. Assuming that the true population mean is 5.2, determine the probability of committing an error of Type II error. A. 0.8413 B. 0.05 C. 0.9332 D. 0.8943 E. none of the preceding 78. [1] True or False Question A new treatment has been developed for a certain type of cement. To test the null hypothesis that μ = 5000 against the alternative that μ 6 = 5000, where μ is the mean resistance in kg/cm 2 , a sample of 50 samples of cement is examined and we observe x = 4775 and s = 130. At α = 0 . 05, the evidence against the null hypothesis in favour of the alternative hypothesis is significant. True False 79. [1] True or False Question An engineer measures the weights (in kilograms) of steel pieces. They would like to test H 0 : μ = 5 against H 1 : μ > 5. The weight of a steel piece is normally distributed. They select a random sample size of n = 25 steel pieces, and compute x = 6 . 7 and s = 2 . 37. We cannot conclude that the mean weight is larger than 5 kg at a level of significance of 1%. True False 80. [1] True or False Question In order to establish a control chart for the mean of a process, 20 samples each of size 4 are collected. We note that ∑ 20 i =1 x i = 4000 and ∑ 20 i =1 s i = 500. The value of the lower control limit of the chart for the mean is approximately equal to 195.5. True False 81. [1] True or False Question In order to establish a control chart for the mean of a process, 20 samples each of size 4 are collected. We note that ∑ 20 i =1 x i = 4000 and ∑ 20 i =1 s i = 500. The value of the lower control limit of the chart for the mean is approximately equal to 183. True False

MAT 2377 Final Exam - Page 21 of 37 April 20, 2020 82. [1] True or False Question In order to establish a control chart for the mean of a process, 20 samples each of size 4 are collected. We note that ∑ 20 i =1 x i = 4000 and ∑ 20 i =1 s i = 500. The value of the upper control limit of the chart for the mean is approximately equal to 217. True False 83. [1] True or False Question The length of time in minutes between consecutive calls to 911 in a small city has density f ( x ) = 1 20 e - x/ 20 0 < x < ∞ 0 otherwise The probability that the time between consecutive calls is greater than 20 minutes is thus 1 /e . True False 84. [1] True or False Question A boiler has 4 relief valves which operate independently. The probability that each opens properly is 0 . 99. The probability that at least one opens properly is thus 1 - (0 . 99) 4 . True False 85. [1] True or False Question In order to establish a control chart for the mean of a process, 20 samples each of size 4 are collected. We note that ∑ 20 i =1 x i = 4000 and ∑ 20 i =1 s i = 500. The value of the upper control limit of the chart for the mean is approximately equal to 204.5. True False 86. [1] True or False Question A random sample of 100 urban residents reveals that 50 believe in angels whereas in a random sample of 100 rural residents it is found that 65 believe in angels. We test the null hypothesis that the percentage of urban and rural residents who believe in angels is the same against the alternative that it is higher for rural residents. Based on this data, the corresponding test statistic is 2 . 165 and we reject the null hypothesis at a significance level α = 10%. True False MAT 2377 Final Exam - Page 22 of 37 April 20, 2020 87. [1] True or False Question The percentage of males in 1986 who are 18-19 years old and married was 3 . 7%. To test whether or not this percentage had increased in 2015, a random sample of 300 males aged 18-19 was taken; 20 of which were married. Using a level of significance of α = 0 . 05, we test the hypothesis H 0 that the proportion that is married is 3 . 7% against the alternative that it is larger. Based on the data, the observed value of the corresponding test statistic is 2 . 722 and we reject H 0 . True False 88. [1] True or False Question A postmix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was found to have a mean syrup content of 1 . 05 fluid ounces and a standard deviation of 0.15 fluid ounces. Assume that the syrup content of a beverage is normally distributed. Then, to check the claim that the syrup content per beverage is about one ounce, we use the following test H 0 : μ = 1 against H 1 : μ 6 = 1 . Based on the samples, the p - value for the test is less than 0 . 05. True False 89. [1] True or False Question A candy maker produces mints whose weight follows a normal distribution with mean 21 . 37g and standard deviation 0 . 4g. Suppose 15 mints are selected at random. Let Y be the number of mints among them that weigh less than 20 . 857g. Then, P ( Y ≤ 2) = 0 . 816. True False 90. [1] True or False Question Students on a boat have 9 flags to arrange on a pole. There are 3 red, 4 yellow and 2 blue flags. Flags of the same colour are indistinguishable. A total of 1524 different signals can be sent by arranging all the 9 flags on the pole. True False 91. [1] True or False Question Let X, Y be independent random variables with E[ X ] = E[ Y ] = 0 and σ X = σ Y = 5. Then Var( 2 X +3 Y 5 ) = 1. True False

MAT 2377 Final Exam - Page 25 of 37 April 20, 2020 100. [2] Short Answer Question We have a dataset with n = 10 pairs of observations ( x i , y i ), and n X i =1 x i = 683 , n X i =1 y i = 813 , n X i =1 x 2 i = 47 , 405 , n X i =1 x i y i = 56 , 089 , n X i =1 y 2 i = 66 , 731 . What is an approximate 99% confidence interval for the mean response at x 0 = 90? 101. [2] Short Answer Question We have a dataset with n = 10 pairs of observations ( x i , y i ), and n X i =1 x i = 683 , n X i =1 y i = 813 , n X i =1 x 2 i = 47 , 405 , n X i =1 x i y i = 56 , 089 , n X i =1 y 2 i = 66 , 731 . What is an approximate 99% confidence interval for the mean response at x 0 = 90? 102. [2] Short Answer Question We have a dataset with n = 10 pairs of observations ( x i , y i ), and n X i =1 x i = 683 , n X i =1 y i = 813 , n X i =1 x 2 i = 47 , 405 , n X i =1 x i y i = 56 , 089 , n X i =1 y 2 i = 66 , 731 . What is an approximate 95% prediction interval for the response y 0 at x 0 = 60? 103. [2] Short Answer Question We have a dataset with n = 10 pairs of observations ( x i , y i ), and n X i =1 x i = 683 , n X i =1 y i = 813 , n X i =1 x 2 i = 47 , 405 , n X i =1 x i y i = 56 , 089 , n X i =1 y 2 i = 66 , 731 . What is an approximate 95% prediction interval for the response y 0 at x 0 = 90? MAT 2377 Final Exam - Page 26 of 37 April 20, 2020 104. [2] Short Answer Question We have a dataset with n = 10 pairs of observations ( x i , y i ), and n X i =1 x i = 683 , n X i =1 y i = 813 , n X i =1 x 2 i = 47 , 405 , n X i =1 x i y i = 56 , 089 , n X i =1 y 2 i = 66 , 731 . What is an approximate 99% prediction interval for the response y 0 at x 0 = 60? 105. [2] Short Answer Question We have a dataset with n = 10 pairs of observations ( x i , y i ), and n X i =1 x i = 683 , n X i =1 y i = 813 , n X i =1 x 2 i = 47 , 405 , n X i =1 x i y i = 56 , 089 , n X i =1 y 2 i = 66 , 731 . What is an approximate 99% prediction interval for the response y 0 at x 0 = 90? 106. [2] Short Answer Question We have a dataset with n = 10 pairs of observations ( x i , y i ), and n X i =1 x i = 683 , n X i =1 y i = 813 , n X i =1 x 2 i = 47 , 405 , n X i =1 x i y i = 56 , 089 , n X i =1 y 2 i = 66 , 731 . What is the mean squared error estimate for the variance of the residuals? 107. [2] Short Answer Question We have a dataset with n = 10 pairs of observations ( x i , y i ), and n X i =1 x i = 683 , n X i =1 y i = 813 , n X i =1 x 2 i = 47 , 405 , n X i =1 x i y i = 56 , 089 , n X i =1 y 2 i = 66 , 731 . What is the line of best fit for this data?

MAT 2377 Final Exam - Page 27 of 37 April 20, 2020 108. [2] Short Answer Question We have a dataset with n = 10 pairs of observations ( x i , y i ), and n X i =1 x i = 683 , n X i =1 y i = 813 , n X i =1 x 2 i = 47 , 405 , n X i =1 x i y i = 56 , 089 , n X i =1 y 2 i = 66 , 731 . What is the coefficient of correlation for this data? 109. [2] Short Answer Question We have m = 5 preliminary samples of size n = 3 (some numbers have unfortunately been erased by accident by a clumsy co-op student): i x i, 1 x i, 2 x i, 3 ¯ x i r i s i 1 27.1 29.4 27.9 1.3 2 30.6 32.5 32.4 31.83 1.9 1.07 3 25.7 35.5 30 30.4 4.91 4 31.1 23.2 25 26.43 7.9 5 24.1 34.2 27.4 28.57 10.1 5.15 total: 145.13 32 16.57 What is the control chart (give the interval) for X from R ? 110. [2] Short Answer Question We have m = 5 preliminary samples of size n = 3 (some numbers have unfortunately been erased by accident by a clumsy co-op student): i x i, 1 x i, 2 x i, 3 ¯ x i r i s i 1 27.1 29.4 27.9 1.3 2 30.6 32.5 32.4 31.83 1.9 1.07 3 25.7 35.5 30 30.4 4.91 4 31.1 23.2 25 26.43 7.9 5 24.1 34.2 27.4 28.57 10.1 5.15 total: 145.13 32 16.57 What is the control chart (give the interval) for X from S ?