2 Assignment 2 consists of a theory component (2A, worth 80%) and a computer component (2B, worth 20%). The grades allocated are summarized below. Assignment Grade weight Assignment 2A. Theory component 60 marks 80% Assignment 2B. Computer component 15 marks 20% Total marks 75 marks 100% You must submit Assignment 2A and Assignment 2B together as PDFs, through the appropriate drop box on the course home page. Submit: 1. One PDF solution file (file) entitled Assignment2A containing all your answers to Assignment 2A, presented in the proper order. Your name and student ID number must be at the top of the first page of your solution file. and 2. One PDF solution file (file) entitled Assignment2B containing all your answers to Assignment 2B, presented in the proper order. We suggest that you print the Assignment 2 questions, so that you can conveniently review the questions with their solutions when you prepare for your exams. Computer-oriented Approach to Statistics 1 Assignment 2A. Theory Component Show your work for this component. Where relevant and unless otherwise instructed, keep your calculations and your final answer to at least four decimals. Problem 1. University survey The table below summarizes the results of a survey that asked 5000 faculty and students at a Canadian university whether they support a proposed ban on the sale of junk food (chips, pop, candy, and chocolate bars) on campus. Support Oppose Neutral Total Faculty 250 40 10 300 Students 1000 3500 200 4700 Total 1250 3540 210 5000 Figure 1. Survey data. If one of the 5000 individuals surveyed is selected at random: a. Find the probability that the individual selected opposes the proposed ban. [2 marks] b. Find the probability that the individual selected is a student. [2 marks] c. Find the probability that the individual selected is a student and opposes the proposed ban. [2 marks] d. Find the probability that the individual selected is faculty or supports the proposed ban. [3 marks] e. Find the probability that the individual selected is a student given that the individual selected opposes the proposed ban. [2 marks] f. Find the probability that the individual selected supports the proposed ban given that the individual selected is faculty. [2 marks] g. Are the events \"being a student\" and \"support the proposed ban\" mutually exclusive events? Explain. [2 marks] h. Are the events \"being a student\" and \"oppose the proposed ban\" independent events? Determine the answer by showing the appropriate math work. [4 marks] 2 Mathematics 216/ Assignment 2 Problem 2. Shirts sold In analyzing the sales of the last 200 dress shirts sold at a large men's wear retail outlet, the manager created the following frequency table. Shirt Size Frequency Small 15 Medium 70 Large 85 Extra Large 30 Figure 1. Frequency table. When the next customer walks in to buy a dress shirt, find the probability that: a. The customer will buy a large dress shirt. [2 marks] b. The customer will not buy a small dress shirt. [2 marks] c. What type (concept) of probability are you using in determining your answer to part a above? Briefly explain. [2 marks] Problem 3. Jobs-for-All The owner of Jobs-for-All, a privately run job readiness program, publicly claims that anyone who has successfully completed this program will have a 90% chance of finding full-time employment within a month after graduating. To investigate the owner's claim, a consumer protection agency contacted three people, at random, who had successfully completed Jobs-for-All. The agency was careful to ensure that these three people were contacted one month after graduating from the program. Assuming that the owner's claim is accurate, compute the following probabilities. a What is the probability that all three people contacted obtained full-time jobs? [4 marks] i. What is the probability that none of the three people contacted obtained full-time jobs. [4 marks] j. What is the probability that at least one of the three people contacted obtained full-time work? [4 marks] Problem 4. Curling competition Computer-oriented Approach to Statistics 3 Twenty curling teams (each representing a different country) are competing for gold, silver, and bronze medals in a week-long world tournament. In how many different ways can the curling teams win gold, silver, and bronze? [4 marks] Problem 5. Lottery In a popular local lottery, you must select 3 numbers (in any order) correctly out of a possible 25 numbers to win the top prize. If you purchase one ticket (with your three numbers on it), what is the probability of your winning the top prize? Keep your final answer to six decimals. [4 marks] Problem 6. Major Motors Major Motors sells both new and used cars. Past sales records show the following customer purchasing behaviour: 60% of all sales tend to be of new cars, and 40% of used cars. When a new car is sold, there is a 50% chance that the customer will purchase an extended car warranty. When a used car is sold, there is a 75% chance that the customer will purchase an extended car warranty. A new customer is about to purchase a car from Major Motors. As the salesman, you would like to look at all possibilities in terms of the person buying a used or new car with or without the extended warranty. a Draw a tree diagram to illustrate all possible customer purchase outcomes in terms of the customer buying a used or new car with or without the extended warranty. [3 marks] k. Find the probability that the new customer will purchase a new car and the extended warranty. [4 marks] l. Find the probability that the new customer will purchase an extended warranty. [4 marks] m. Determine if the two events \"buys a new car\" and \"purchases an extended warranty\" are independent. [4 marks] Assignment 2B. Computer Component As you work through each computer problem, use StatCrunch to generate all computerrelated solutions. Do not round off the results you get from StatCrunch. Make sure that, for each computer problem, you copy and paste the output generated by StatCrunch (as is) as requested, into a single word processing file called Assignment2B. Use a word processing program that allows you to convert to a PDF file after you have completed all your solutions. 4 Mathematics 216/ Assignment 2 Make sure that you type the appropriate problem subheading (e.g., Problem 7a) before you copy and paste the related StatCrunch output or type solutions to the related interpretation questions in the Assignment2B word processing file. Each time you make a change to a StatCrunch file or word processing file, be sure to save the file. Computer-oriented Approach to Statistics 5 Problem 7. SumDice: At least 8/Less than 8 Open a new StatCrunch blank Data table. a Consider the following probability experiment. Two dice are tossed, and you are interested in observing the total of the two numbers that come up on the dice. For example, if a pair of ones (1,1) appears, the total is 2. If the two dice show a 5 on the first die and 3 on the second die (5,3), the total is 8. Use StatCrunch to simulate this probability experiment of tossing a pair of dice simultaneously 1,000 times. In the process, you will use random numbers to generate two column variables: \"Die1\" and \"Die2\". You will then create a third variable column called \"Die1 + Die2\" by using StatCrunch to compute the appropriate Expression. After generating the variable column \"Die1+Die2\