Transcript Week 7
PROBABILITY AND STATISTICS WEEK 7 Onur Doğan 2016-2017 Quiz Q1 • How many positive integer solutions are there to the equation x+y+z=12? Onur Doğan 2016-2017 Quiz Q2 • After all students have left the classroom, a statistics professor notices that three bags were left under desks. At the beginning of the next lecture, the professor distributes the three bags in a completely random fashion to each of the three students who claim to have left bags. Let X denote the number of students who receive their own bag. Determine the pmf of X. Onur Doğan 2016-2017 Quiz Q3 • The pmf for X=the number of major defects on a randomly selected appliance of a certain type is • Calculate the E(X) and V(X). Onur Doğan 2016-2017 Quiz Q4 • Customers are used to evaluate preliminary product designs. In the past, 95% of highly successful products, 60% of moderately successful products, and 10% of poor products received good reviews. In addition, 40% of product designs have been highly successful, 35% have been moderately successful, and 25% have been poor products. i.Find the probability that a product receives a good review. ii.What is the probability that a new design will be highly successful if it receives a good review? Onur Doğan 2016-2017 Binomial vs Hypergeometric Onur Doğan 2016-2017 Onur Doğan 2016-2017 Binomial vs Hypergeometric Onur Doğan 2016-2017 Example • A basketball player has a free throw percentage of 70%. In a single game, the player shoots 6 free throws. Compute the following probabilities. • i. What is the probability that she makes exactly 3? • ii. What is the probability that she makes at least 5 successful throws? • İii.What is the probability that she makes all 6? Onur Doğan 2016-2017 Example • During a particular period a university’s information technology office received 20 service orders for problems with printers, of which 8 were laser printers and 12 were inkjet models. A sample of 5 of these service orders is to be selected for inclusion in a customer satisfaction survey. What’s the probability of 2 of the selected printers are inkjet models? Onur Doğan 2016-2017 Example • Products produced by a machine has a 3% defective rate. i.What is the probability that the first defective occurs in the fifth item inspected? ii.What is the probability that the first defective occurs in the first five inspections? Onur Doğan 2016-2017 Example • A team is currently winning 0,6 of their games. There are 5 games in November. What is the probability that the team will win more games than they lose? Onur Doğan 2016-2017 Example • A person conducting telephone surveys must get 3 completed surveys before their job finished. There is 0,1 chance of reaching a person who will complete the survey. What is the probability the 3 completed survey occurs on the 10th call? Onur Doğan 2016-2017