5 questions: probability of success, standard dev, reliability, goodness-of-fit


Thank you so much for a forum to help folks out! My husband is studying for his ASQ CQE test. (American Society for Quality's Certified Quality Engineer.) He is studying from a few sample CQE tests. Most of the questions he has been able to figure out for himself. Others I've been able to Google to find answers. However, there are four questions that he is not sure the correct way to solve. I would be most grateful if you might help us figure out how these problems are solved.

Unfortunately, I am not a statistician but he is unable to access the Internet where he is, so forgive me if I use the wrong lingo. It would be wonderful if you could offer the solutions, but even guidelines (like using z tables or student's t tables) would be helpful.

1. A process with a binomial distribution has a 5% probability of success. If 10 samples are drawn from the process, what is the approximate probability of having zero success? (2011 Sample Test, Question 61, page 13)

2. A data set for a measured characteristic of a part has a standard deviation of 11.2. If the standard deviation of the measurement error is 2.1, what is the estimated true standard deviation for the characteristic? (2011 Sample Test, Question 56, page 13)

3. In a complex electronic system containing 1,000 devices in series, an increase in component reliability from 99.90% to 99.99% would improve the system reliability by a factor of approximately: (2011 Sample Test, Question 54, page 13)

4. A sample of 50 pieces is taken from a process that is known to be producing .2% non-conforming pieces. The probability that non-conforming pieces will NOT be found in the sample is approximately equal to? (2011 Sample Test, Question 46, page 12)

5. An internet service provider logged four primary types of complaints over a one-month period. A team used the data to create the following incomplete table. [Please see the sample test for the table.] What test statistic should be used in a goodness-of-fit analysis? (2011 Sample Test, Question 74, page 15)

2004 CQE Sample Test: http://www.ocot.ca/docs/cqe_exam.pdf
2011 CQE Sample Test: https://asq.org/cert/resource/pdf/sample-exam/cqe-sample-exam.pdf