STAT 200 QUIZ 2 VERIFIED A+

STAT 200 QUIZ 2 I have completed this assignment myself, working independently and not consulting anyone except the instructor. INSTRUCTIONS • The quiz is worth 40 points total. • The quiz covers week 3 and week 4 materials. • Make sure your answers are as complete as possible and show your work/argument. When there are calculations involved, you should show how you come up with your answers with critical work and/or necessary tables. You must show why you choose certain answer for true-or-false and multiple choice questions. Answers that come straight from program software packages will not be accepted. • The quiz is open book and open notes. This means that you may refer to your textbook, notes, and online course materials, but you must work independently and may not consult anyone. The brief honor statement is on top of the exam. If you fail to put your name under the statement, your quiz will not be accepted. You may take as much time as you wish, provided you turn in your quiz via LEO by 11:59 pm EDT on Sunday, September 25. 1. (8 points) Assume that you toss a fair six-faced die two times. (a) (1 pt) How many possible outcomes are in the sample space? Explain your answer. 36 outcomes – I counted these out. (b) (1 pt) What is the probability that you get a number greater than 3 at the first toss? (Show work and write the answer in simplest fraction form) P(>3 – 1st) = 18/36 = ½ There are 18 chances that we could roll a number greater than 3 on the first toss (see my lovely picture), divided by the total number of possibilities, which is 36. (c) (2 pts) What is the probability that the sum of the two tosses is at least 9? (Show work and write the answer in simplest fraction form) P(Sum>9) = 10/36 = 5/18 There are 10 chances that the sum of the two tosses is at least 9, divided by the total number of possibilities, which is 36. (3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6) (d) (2 pts) What is the probability that the sum of the two tosses is at least 9, given that you get a number greater than 3 in the first toss? (Show work and write the answer in simplest fraction form) P(A|B) = P(A&B)/P(B) = 5/9 P(Sum>9|1st>3) = (5/18)/(18/36) = (5/18)/(1/2) = (5/18)x(2/1) = 10/18 = 5/9 There is a 5/18 chance that the sum of the two tosses is at least 9, and there is a ½ chance that you get a number greater than 3 in the first toss. (e) (2 pts) If event A is “Getting a number greater than 3 in the first toss” and event B is “The sum of two tosses is at least 9”. Are event A and event B independent? Use statistical concept and mathematical expression to justify your answer. In this case, event A and event B are not independent. This is an example of conditional probability, given what we know from 1D. Event B depends on the draw of event A. 2. (2 points) A high school with 1000 students offers two AP courses: Statistics and Calculus. There are 150 students in the Calculus class roster, and 250 students in the Statistics class roster. We also know that 80 students enroll in both courses. Find the probability that a randomly selected student takes neither AP course. (Show work and write the answer in simplest fraction form) 17/25 3. (2 points) The steering committee of UMUC Green Solutions Team consists of 5 committee members