MATH26367_Midterm_vB_F2016

MATH 26367 Statistical Methods Fall 2016 MATH 26367 Statistical Methods – Midterm B INSTRUCTOR: Stephane Lemieux DATE : Tuesday, Oct. 18 th , 2016 DURATION : 90 minutes (40 total marks, 25% of the overall course grade) STUDENT NAME: SLATE USER ID: PART 1: Multiple choice questions, circle the best answer. 1 mark each, 5 total. 1. The following table provides information on 2 of the 105 earthquakes that occurred on May 10, 2013. Magnitude was measured using the Richter scale and NST stands for the number of stations that reported the activity of the same earthquake. Time NST Depth (km) Magnitude Region 03:46:54 25 16.7 1.6 N. California 15:19:57 11 7.7 1.8 Tennessee Which column in the table above contains discrete, quantitative data ? a. Time b. NST c. Depth d. Magnitude e. Region 2. Which of the following best describes the skew of the graph below? a. Symmetric b. Positive skew c. Skewed left d. Negative skew Midterm exam Page 1 of 9

MATH 26367 Statistical Methods Fall 2016 3. Which if the following images displays the highest degree of positive correlation? a. b. c. d. e. 4. A computer crashes once every two days on average. What is the most accurate experimental model that you can use to determine the probability of the computer crashing twice in one week? a. Normal b. Binomial c. Poisson d. None of the above 5. The grades for a statistics quiz are normally distributed with a mean grade of 58 and a standard deviation of 8. If a passing grade is 50, apply the empirical rule to calculate how many students passed the quiz if the class has 25 students? a. 13 b. 15 c. 17 d. 19 e. 21 Midterm exam Page 2 of 9

MATH 26367 Statistical Methods Fall 2016 2. The chief of IT security has asked you to estimate next quarter’s budget based on the following data: (5 marks total) Quarter Months in Operation Budget (in $000’s) Months x Budget Months^2 2015 Q3 3 58 174 9 2015 Q4 6 75 450 36 2016 Q1 9 61 549 81 2016 Q2 12 77 924 144 2016 Q3 15 75 1125 225 2016 Q4 18 80 1440 324 Sum 63 426 4662 819 Average 10.5 71 777 136.5 You decide to do regression using months in operation and budget. a. What is the slope of your regression line? (2 marks) b. What is the intercept of your regression line? (2 marks) c. What is your estimate of next quarter’s (2017 Q1) budget? (1 mark) Midterm exam Page 4 of 9

MATH 26367 Statistical Methods Fall 2016 3. The chart below lists the number of cyber events and incidents logged for your company in each of the last 15 months. (10 marks total) Month Number of Events Incidents (X) ( X − X ) 2 Aug-15 1357 116 576 Sep-15 1237 104 144 Oct-15 1227 115 529 Nov-15 1177 116 576 Dec-15 1128 117 625 Jan-16 1061 91 1 Feb-16 1061 91 1 Mar-16 985 91 1 Apr-16 970 81 121 May-16 881 70 484 Jun-16 795 86 36 Jul-16 754 77 225 Aug-16 741 71 441 Sep-16 717 62 900 a. Draw a Stem-Leaf plot of the number of Incidents per month . (3 marks) b. Circle the mode on the plot? (1 marks) Midterm exam Page 5 of 9

MATH 26367 Statistical Methods Fall 2016 4. A block of IP addresses, originating from Russia, regularly communicates with your company’s main server. The start times of the activity is normally distributed with an average start time of 3:45 am with a standard deviation of 45 minutes, (i.e. σ = 0.75 hours). (4 marks total) a. What is the probability that the activity will start after the company’s business day has started at 6:00 am? (2 marks) b. If the activity always lasts exactly 30 minutes, what is the probability that the cleaning crew, arriving at 5:00am, will arrive before the activity stops? (2 marks) Midterm exam Page 7 of 9

MATH 26367 Statistical Methods Fall 2016 5. Each account at your company experiences an average of 1 failed login attempt per day. For a single account: (5 marks total) a. What is the probability of witnessing exactly 6 failed login attempts in a 5-day workweek? (2 marks) b. What is the probability of witnessing at least 2 failed login attempts in a 5-day workweek? (2 marks) c. As IT security chief you want to establish a rule that if N or more failed login attempts are observed in a single day and on a single account; then the behaviour needs to be investigated. You want to ensure that the probability of seeing less than N failed attempts, by random chance, is at least 95%. (i.e. there is at most a 5% chance of witnessing N or more failed attempts by random chance.) What N should you chose based on the table below? (1 mark) Number of failed login attempts Probability of exactly that number occurring by random chance 0 0.3679 1 0.3679 2 0.1839 3 0.0613 4 0.0153 5 0.0031 6 0.0005 Midterm exam Page 8 of 9