Binomial and Geometric Distributions Homework Solutions - 184 Chapter 8 Chapter 8 8.1 Not binomial There is not fixed number of trials n(i.e there is no

# Binomial and Geometric Distributions Homework Solutions -...

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Chapter 8 8.1 Not binomial: There is not fixed number of trials n (i.e., there is no definite upper limit on the number of defects) and the different types of defects have different probabilities. 8.2 Yes: 1) “Success” means person says “Yes” and “failure” means person says “No.” (2) We have a fixed number of observations ( n = 100). (3) It is reasonable to believe that each response is independent of the others. (4) It is reasonable to believe each response has the same probability of “success” (saying “yes”) since the individuals are randomly chosen from a large city. 8.3 Yes: 1) “Success” means reaching a live person and “failure” is any other outcome. (2) We have a fixed number of observations ( n = 15). (3) It is reasonable to believe that each call is independent of the others. (4) Each randomly-dialed number has chance p = 0 . 2 of reaching a live person. 8.4 Not binomial: There is no fixed number of attempts ( n ). 8.5 Not binomial: Because the student receives instruction after incorrect answers, her probability of success is likely to increase. 8.6 The number who say they never have time to relax has (approximately) a binomial distribution with parameters n = 500 and p = 0 . 14. 1) “Success” means the respondent “never has time to relax” and “failure” means the respondent “has time to relax.” (This is a good example to point out why “success” and “failure” should be referred to as labels.) 2) We have a fixed number of observations ( n = 500). 3) It is reasonable to believe each response is independent of the others. 4) The probability of “success” may vary from individual to individual (think about retired individuals versus parents versus students), but the opinion polls provide a reasonable approximation for the probability in the entire population. 8.7 Let X = the number of children with type O blood. X is B(5, 0.25). 5 3 2 3 2 ( 3) (0.25) (0.75) 10(0.25) (0.75) 0.0879 3 P X = = = ± 8.8 Let X = the number of broccoli plans that you lose. X is B(10, 0.05). ( ) ( ) ( )( ) 9 10 10 0 10 1 ( 1) 0 1 (0.05) (0.95) (0.05) (0.95) 0 1 10 (0.95) 10 0.05 0.95 0.9139 P X P X P X = = + = = + = + ± 9 8.9 Let X = the number of children with blood type O. X is B(5, 0.25). 5 0 5 5 ( 1) 1 ( 0) 1 (0.25) (0.75) 1 (0.75) 1 0.2373 0.7627 0 P X P X = = = = = ± 8.10 Let X = the number of players who graduate. X is B(20, 0.8). 184 Chapter 8