BADM 216.D46 Fall 2016 Mid-term Exam (Part 2) 1. The closing stock price of Ahmadi, Inc. for a sample of 10 trading days is shown below. Day 1 2 3 4 5 6 7 8 9 10 Stock Price 77 84 88 76 90 91 83 92 86 For the above sample, compute the following measures. a. The mean b. The median c. The mode d. The range [Hint: Please see Chap003A - Slide 5, 8, 15, 22, and 32 for formula and examples.] 2. Based on the information, please compute the following measures: Daily Supply Unit Price (x) (y) 7 4 9 8 12 5 10 7 16 6 (1) Mean for variable y and for x. 1 (2) Standard deviation for variable y and for variable x. (3) Sample correlation coefficient for variable y and x. [Hint: Please see Chap003A - Slides 35 - 38 for formula of standard deviation. Please see page 124 - 125 in the textbook. Please see Chap003B - Slides 33 - 38 for formula of correlation coefficient. Please also see page 146 - 148 in the textbook. ] 3. (1) Suppose that, from 11 students, we want to take a committee of students. How many committees consisting of 3 students can be selected? How many committees consisting of 4 students can be selected? (2) Suppose we want to select 3 out of 11 students and give them the first and second and third places. Determine the number of possible selections? [Hint: Please see Chap004 - Slide 13 for formula of Combination. Please also see page 182 in the textbook. Please see Chap004 - Slide 14 for formula of Permutation. Please also see page 182183 in the textbook.] 4. As a company manager for Claimstat Corporation there is a 0.40 probability that you will be promoted this year. There is a 0.72 probability that you will get a promotion, a raise, or both. The probability of getting a promotion and a raise is 0.25. (1) If you get a promotion, what is the probability that you will also get a raise? (2) What is the probability that you will get a raise? (3) Are getting a raise and being promoted independent events? Explain using probabilities. 2 (4) Are these two events mutually exclusive? Explain using probabilities. [Hint: Please see Chap004 - Slides 28 - 29 for definition of union of events, and see Slides 30 - 31 for definition of intersection of events. Please see Slides 32 - 33 for Addition Law. Please see Slides 34 - 35 for Mutually Exclusively events. Please also see pages 193 - 196 in the textbook. Please see Slides 41 - 43 for Independent events. Please also see pages 202 - 203 in the textbook.] 5. The following table shows the number of students in three different degree programs and whether they are graduate or undergraduate students: Business Engineering Arts & Sciences Total Undergraduat Graduate Total e 150 50 200 150 25 175 100 25 125 400 100 500 (1 What is the probability that a randomly selected student is ) an undergraduate? (2 What percentage of students is engineering majors? ) (3 Given that a selected student is an undergraduate, what is ) the probability that he or she is a business major? [Hint: Please see Chap004 - Slide 40 for Joint probability table. Please also see pages 199 - 200 in the textbook.] 3 6. Suppose the event of a student's application to a university being accepted follows the binomial probability and the successful rate is 70%. Please finish the following tasks? (1) Determine the expected number of acceptances for the next 10 applicants and the standard deviation. (2) What is the probability that among the next 10 applicants exactly 8 will be accepted? [Hint: Please see Chap005 - Slides 27 -39 for Binomial Probability Distribution. Please also see pages 237 - 245 in the textbook.] (Extra Credit) 7. The random variable x is the number of occurrences of an event over an interval of ten minutes. Suppose x follows a Poisson distribution with the mean number of occurrences in ten minutes is 5. (1) Based on the data given, what is the expected value of the random variable x in next 20 minutes? (2) What is the probability that there are 8 occurrences in ten minutes? (3) Based on the data given, what is the probability that there are less than 3 occurrences in ten minutes? [Hint: Please see Chap005 - Slides 40 -49 for Poisson Probability Distribution. Please also see pages 248 - 251 in the textbook.] Please type your answer and the steps of computation in a Word file. (Please DO NOT just write the answer. Show the steps that you solve the problems. Partial credit will be given based on your computation steps.) Please save the file as 4 \"BADM216D46-MidtermPart2_Your First Name_Your Last Name.docx\" and submit through Canvas. Due Date: November 3rd, 2016, Thursday, 11:00PM. 5