MATH 534 Week 2 Homework Problems

1. Question: If the occurrence or non occurrence of one event does not affect the occurrence or non occurrence of another event, the two events are ___________ . 2. Question: In any statistical experiment if the occurrence of one event precludes the occurrence of the other events, the events of the experiment are called _______ . 3. Question: In the experiment of a single roll of a 6-faced die, if the outcome “3 shows up” is called event A and the outcome “4 shows up” is called event B, then A and B are _________. 4. Question: Fifty percent of all technical assistants would like to have a PC. Eighty percent of all technical assistants would like to have MAC. Fourty-five percent of all technical assistants would like to have both. If a technical assistant is randomly selected, what is the probability that she would like to have a PC or a MAC? 5. Question: Consider the following 3 x 4 contingency table in which a sample of 1400 companies is summarized in terms of the company’s industry type (X, Y, or Z) and geographic location (A, B, C, or D). 6. Question: If two events, Event A with probability P(A) and Event B with probability P(B) are independent, then . 7. Question: An article titled” Pain and Pain related side effects in an ICU and on a surgical unit: Nurses’ Management” (American Journal of Critical Care, January 1994, Vol 3, No:1) gave the following table summarizing the study participants. (Note that ICU is an acronym for Intensive care unit. Given this person is a female, what is the probability that she is from ICU? 8. Question: Consider the following 3 x 4 contingency table in which a sample of 1400 companies is summarized in terms of the company’s industry type (X, Y, or Z) and geographic location (A, B, C, or D). What is the probability P(B│Y)? 9. Question: There is a 30% chance that the economy will be good next year and a 70% chance that it will be bad. If the economy is good, there is a 60% chance of a bull market, a 30% chance of a normal market, and a 10% chance of a bear market. If the economy is bad, there is a 15% chance of a bull market, 30% chance of a normal market, and a 55% chance of a bear market. What is the probability of having a good economy and a bull market? 10. Question: There is a 30% chance that the economy will be good next year and a 70% chance that it will be bad. If the economy is good, there is a 60% chance of a bull market, a 30% chance of a normal market, and a 10% chance of a bear market. If the economy is bad, there is a 15% chance of a bull market, 30% chance of a normal market, and a 55% chance of a bear market. Given the market is a normal market next year, what is the probability that the economy is good? 11. Question: In a sample of ten students randomly selected from your class, the height of student is ____________. 12. Question: The average time of students spend on reading per day is ______. 13. Question: Consider the following discrete random distribution. 14. Question: What is the mean of the distribution? 15. Question: Joe throws a die 4 times, what is the probability of him getting a number 1 at most once? 16. Question: What is the mean of a binomial distribution in which the number of trials n = 100 and the probability of success p = 0.5? 17. Question: A dealer in a casino has rolled a 6 on a single die four times in a row. What is the probability of his rolling another 6 on the next roll, assuming it is a fair die? 18. Question: The expected number of defectives in samples of 200 units taken periodically from the output of a machine that has a 0.5% defective rate is _____________. 19. Question: One fair coin is tossed 10 times, what is the probability of getting exactly 3 heads out of 10 tossing experiments? 20. Question: Use Table A.2, Appendix A, to find the values of the following binomial distribution problems. 21. Question: According to the American Medical Association, about 36% of all U.S. physicians under the age of 35 are women. Your company has just hired eight physicians under the age of 35 and none is a woman. If a group of women physicians under the age of 35 want to sue your company for discriminatory hiring practices, would they have a strong case based on these numbers? Use the binomial distribution to determine the probability of the company’s hiring result occurring randomly, and comment on the potential justification for a lawsuit