BUSI1450 - Statistics (F2017) Assignment #2 Questions DUE: Thursday, November 2, 2017 before midnight (AKA 11:59 PM) Please review and follow submission guidelines (posted in Assignments folder). DO NOT submit this file as your submission - please create a NEW \"Word\" document for your submission - you do not need to include the text of the questions in your submission; only your responses are needed. There are 15 questions in this assignment, totaling 44 marks. Questions 1 through 6 are multiple choice. 1. (1 pt.) Which one of the following statements is false? a. Each distinct observation that results from an experiment is called an outcome. b. A certain event will have a probability between 0 and 1. c. The set of all possible outcomes for a given experiment is called the sample space. d. Empirical probability is calculated based on actual observations from experiments that are performed. Use the following table to answer questions 2 through 5. All 410 employees at a company were surveyed as to whether they were female or male and what type of vehicle they drive to work. car 41 52 93 female male total van 82 75 157 SUV 24 38 62 truck 49 49 98 total 196 214 410 2. (1 pt.) What is the probability that a randomly selected employee is a female and drives a van? 82 82 82 157 a. 196 b. 157 c. 410 d. 410 3. (1 pt.) We randomly select one of male employees. What is the probability that he drives a truck? 49 49 49 49 a. 214 b. 196 c. 1 196 d. 410 4. (1 pt.) What is the probability that a randomly selected employee drives an SUV or is a female? 62 196 62 196 24 62 196 24 62 196 24 a. 410 + 410 b. 410 + 410 62 c. 410 + 410 196 d. 410 + 410 410 5. (1 pt.) What is the probability that a randomly selected car driver is not a female? a. 41 93 41 b. 1 93 41 c. 196 41 d. 1 196 BUSI1450 - Statistics (F2017) Assignment #2 Questions DUE: Thursday, November 2, 2017 before midnight (AKA 11:59 PM) 6. (1 pt.) Event A occurs with probability 45% and Event B occurs with probability 63%. Which one of the following statements is the most accurate one about the P(A or B): a. Is equal to 45%+63% b. We need to have more information if A and B are dependent to calculate the probability c. We can calculate the probability with given information only if A and B are independent d. b and c 7. (2 pts.) Tonight the Toronto Maple Leafs is going to play with Edmonton Oilers at the Rogers Center. We know that 80% of people in the stadium are Maple Leafs fans, 15% are Oilers fans, and the remaining 5% do not like hockey at all and they are there just for fun! We randomly select 2 people in the stadium. What is the probability that at least one of them is an Oilers fan? Please report your final answer in percent. 8. Two different technologies are used to discover new ore mines. Technology A detects mines with 90% accuracy, and Technology B detects mines with 85% accuracy. We apply these two technologies, independent from each other to a site in northern Ontario. Calculate the following probabilities in percent: a. b. c. d. (1.5 pts.) both technologies are incorrect (1.5 pts.) Technology A is incorrect but Technology B is correct (1.5 pts.) At least one of the two technologies is correct (1.5 pts.) Both technologies are correct 9. A Statistics course is comprised of 25 1.5-hour sessions. At the beginning of the semester, the course professor says that as a part of evaluation rubric, he will give some pop quizzes. We use the random variable X to denote the total number of pop quizzes given in this course. Answer the following questions assuming that the professor gives a quiz on any of the 25 sessions independent of other sessions and that the probability of giving a quiz on any of the 25 days is 0.2: a. b. c. d. e. (0.5 pts.) Is X a continuous random variable or a discrete random variable? (1 pt.) Fill the blanks with the appropriate values: X~B(___ , ___) (0.5 pt.) What is the expected number of quizzes during the semester? (0.5 pt.) What is the variance of the number of quizzes during the semester? (1 pt.) What is the probability that the professor gives exactly 2 quizzes during the semester? f. (2 pts.) ( 3 5) =? BUSI1450 - Statistics (F2017) Assignment #2 Questions DUE: Thursday, November 2, 2017 before midnight (AKA 11:59 PM) 10. Consider the Statistics course described in the previous question. As the professor does not take attendance, some students skip some classes. One of students flip a coin each morning, and if it is heads (with 50% chance) then he goes to the class, otherwise he sleeps in. Calculate the following probabilities: a. b. c. d. e. (0.5 pts.) The student goes to Lecture 9 (1 pt.) The student goes to Lecture 10, given that he also went to Lecture 9. (1 pt.) The student goes to Lecture 15 and the professor gives a pop quiz on that day (2 pts.) What is the probability that the student writes none of the pop quizzes? (1 pt.) If the random variable Y is the total number of pop quizzes that the student writes during the semester, what is E(Y)? 11. (2 pt.) For every 50 tables produced by Country Kitchens, 4 have to be refinished to correct for mistakes in manufacturing. What is the probability no more than 5% of the tables from an order of 60 tables will have to be refinished? 12. The weight of a newborn baby follows a normal distribution with mean 3500 gr and a standard deviation of 250 gr. If the random variable X is the weight of a newborn, then a. b. c. d. e. (0.5 pts.) Fill the blanks with the appropriate values: X~N(___ , ___) (0.5 pts.) What is the variance of X? (1 pt.) What is the probability that a newborn baby weighs exactly 3200 gr? (1.5 pt.) ( 3750) = ? (1.5 pt.) (3100 3750) = ? 13. Heights of adults are well approximated by the normal distribution. Suppose the population of adult Canadian males has a mean height of 175 centimeters, and a standard deviation of 7.1 centimeters. a. (1pt) What is the probability that a randomly chosen male is at least 183 cms tall? b. (1pt.) What is the standardized value for a height of 170 centimeters? We select a random sample of 5 men and measure their heights. Then, c. (1 pt.) What is the mean of the sample mean distribution d. (1 pt.)What is the standard deviation of the sample mean distribution? e. (1 pt.) What is the probability that the sample mean is greater than 180 centimeters? BUSI1450 - Statistics (F2017) Assignment #2 Questions DUE: Thursday, November 2, 2017 before midnight (AKA 11:59 PM) 14. On average, an SUV burns 12 liters of gas per 100 kilometer, and the standard deviation of the fuel consumption is 2 liters. We randomly select a sample of 100 SUVs and measure their fuel consumption per 100 kilometers. a. (0.5 pts.) What is the distribution of the sample mean? b. (0.5 pts.) What is the probability that the sample mean is equal to 8 liters? c. (2 pts.) What is the probability that the sample mean is less than 11.8 liters? 15. On average, 100 cars enter UOIT Parking per hour on a Monday. a. (1 pt.) What is the expected number of cars that enter the parking lot between 8 am and 9 am on a Monday? b. (1 pt.) What is the standard deviation of number of cars that enter the parking lot between 8:30 am and 9 am on a Monday? c. (1 pt.) What is the probability that 55 cars enter the parking lot between 8:30 am and 9 am on a Monday