\f\fProblem Set 3 Instructions Question 1 has aand b. Question 2 has a, b, , d, and e. Question 3 is a single question. Question 4 has a and b. Question 1 Statistics: Mean and Median Refer to the chart below and the line associated with your assigned number to answer these questions. The data represent your hypothetical walking times for each of the months January - October (10 months). a. Calculate your mean and your median walking time for the 10 months. b. How many minutes would you have to walk in November so that your mean for the 11 months would be 2 percentage points more than your mean for the 10 months? Assigned # January - October 1 247,257,277, 315, 328, 342, 351, 352, 360, 411 2 312, 326, 345, 390, 400, 435, 450, 478, 487, 510 3 125, 136, 147, 148, 159, 168, 210, 245, 278, 301 Instructions Question 2 Probability Refer to the chart below and the line associated with your assigned number to answer these questions. There are two boxes containing only red and purple pens. A pen is randomly chosen from each box. a. Which of these events is most likely to occur? Be sure to show all your calculations. Event 1: choosing a red pen from Box B. Event 2: choosing a purple pen from Box A. Event 3: choosing a red pen from Box A. b. Which of these events is least likely to occur? Be sure to show all your calculations. Event 1: choosing a red pen from Box A. Event 2: choosing a purple pen from Box B. Event 3: choosing a red pen from Box B. c. Name an event where the probability would be 1. d. Name an event where the probability would be 0. e. Name an event where the probability would be 3. Assigned # Box A Box A Box B purple pens red pens purple pens Box B red pens Instructions Question 3 Counting Answer the questions that correspond with your assigned number. 1. On an exam, there are three parts. Part 1 has 5 questions on probability. Part 2 has 6 questions on statistics, and part 3 has 4 questions on logic. You must choose 1 question from each part. How many ways can you choose the three questions? 2. A lunch special has 3 choices from the soup category, 8 choices from the salad category and 3 choices from the dessert category. You must choose one from each category. How many ways can you choose the lunch special. 3. Aresearch project is divided into 3 stages. In stage 1 you must choose a topic from 5 listed topics. In Stage 2 you must find data on your topic from one of 5 listed sources. In stage 3 you must present the data in one of 5 graphical representations. In how many ways can you complete stages 1,2,3. 4. You are planning a vacation and have identified 4 destinations, 3 modes of transportation, 3 months during which you can travel. How many itineraries can you have of one destination, one mode of transportation, and one month in which you will travel. a. A small business is forming an advisory committee. The committee will have 1 person from each of the following groups: Group 1 is the 7 full time employees. Group 2 is the 4 investors. Group 3 the 12 customers who recently made orders. In how many ways can the committee be formed? Question 4 Answer the question that corresponds with your assigned number. If the order in a choice does not matter, then a choice such as F G H is the same as the choice of H F G. The Combination rule applies. If the order in a choice does matter, then a choice such as K L M is different from a choice of M K L. The Permutation rules apply. 1. On a test in a math class there are 8 questions, and you must answer 5 of them. a. How many ways can you choose the 5 questions if the order does not matter? b. How many ways can you choose the 5 questions if the order does matter? 2. In a history class there are 5 projects, and you must complete 2 projects. a. How many ways can you choose the 2 projects if the order does not matter? b. How many ways can you choose the 2 projects if the order does matter? 3. You must select 3 math help websites from a list that contains 6 different websites. a. How many ways can you choose the 3 websites if the order does not matter? b. How many ways can you choose the 3 websites if the order does matter? 4. You must make 5-question tests from a test bank of 8 questions. a. How many tests can you make if the order does not matter? b. How many tests can you make if the order does matter? _i_Four finalists for a job will be chosen from 10 interviewees. a. How many ways can the finalists be chosen if the order does not matter? b. How many ways can the finalists be chosen if the order does matter