Week 3 Homework 1. Name___________________________________-- A shampoo manufacturing process has a 12% probability that a bottle of shampoo will not meet purity specifications. Furthermore, there is a 5% probability that the bottle will improperly filled (over-filled, in which case we are giving away product for free, or under-filled, in which case we are subject to claims of false advertising and fraud). What are the total number of outcomes? What is the probability that a bottle of shampoo will meet all specs? Are the purity and bottle filling outcomes independent? 2. Dr B is teaching 200 students this semester. 60 are taking her Math 107 course, 75 are taking her Stat 230 course, and 50 are enrolled in both courses. What is the probability that that one of her students is taking at least one of these two classes? What is the probability that that a student is taking Stat 230 from her, given that the student is taking Math 107? 3. I have 7 leftover earrings in my jewelry box. How many \"pairs\" of mismatched earrings can be worn from these earrings? 1 4. The following table presents the probability distribution for district sales of cars at for a local distributor. NOTE THAT SALES VALUES ARE HUNDREDS. Sales (100's) 0 1 2 3 4 Probability P(x) 0.20 0.10 0.15 0.35 0.20 How many cars should the manager expect to sell on any given day? What is the standard deviation of the expected number of sales? 2 5. Ten percent of the applications received for a particular position are rejected. What is the probability that among the next 5 applications, less than 2 will be rejected? (You can work this with the table.) Show your work using the template. 6. Suppose it is given that 77% of the graduates of a university are \"excellent in programming.\" For a random sample of 6 students, what is the probability that 4 of these 6 will be \"excellent in programming\"? USE EXCEL TO GET THE PROBABILITY VALUE. Show your work using the template. 3