5-22Harley Davidson, director of quality control at the Kyoto Motor car company, is conducting its monthly automatic transmission review. In the procedure, 10 transmissions are removed from the component stack and checked for manufacturing defects. Over time, only 2% of transmissions have defects (suppose defects occur independently in different transmissions).

a) What is the probability that Harley's sample contains more than two transmissions with factory defections?

b) What is the probability that none of the chosen transmissions will have factory defects?

5-23Diane Bruns is the mayor of a big city. Lately, he has been worrying about the possibility that large numbers of people who collect unemployment insurance may actually have a secret job. Her assistants estimate that 40% of unemployment insurance recipients fall into this category, but Mrs Bruns is not convinced. He asks one of his assistants to do an investigation of 10 randomly taken insurance beneficiaries.

a) If the mayor's assistants are right, what is the likelihood that the investigated individuals will have a job? (Do not use tables.)

b) If the mayor's assistants are correct, what is the likelihood that only three of the investigated individuals have a job? (Do not use tables.)

5-46Glenn Howell, vice president of staff at Standard Insurance, has developed a new training program that is fully adaptable to the pace of users. New employees work in various stages at their own pace of work; the end of the training occurs when the material is approved. Howell's program has been especially effective in accelerating the training process, as an employee's salary during training is only 67% of what he would earn when completing the program. In recent years, the average term of the program has been 44 days, with a standard deviation of 12 days.

1.Find the probability that an employee will terminate the program between 33 and 42 days.

1.What is the probability of completing the program in less than 30 days?

2.Finish it in less than 25 or more than 60 days?

5-49 Maurine Lewis, editor of amajor publishing house, estimates that it takes 11 months on average to complete the process of publishing a book, from having the manuscript to having it without finishing, with a standard deviation of 2.4 months. He thinks that normal distribution describes well the disstrition of publication times. Of 19 books that will work this year, approximately how will they complete the publishing process in less than a year?