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Chapter 3: Q100SE (page 203)
From a production batch with 16 items, 8 items are randomly selected for quality assurance. In how many different ways can the sample be drawn? Suggest an estimate before computing the exact number.
There are 12870 different ways in which the samples can be drawn.
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Randomization in a study of TV commercials. Gonzaga University professors conducted a study of more than 1,500 television commercials and published their results in the Journal of Sociology, Social Work, and Social Welfare (Vol. 2, 2008). Commercials from eight networks—ABC, FAM, FOX, MTV, ESPN, CBS, CNN, and NBC—were sampled for 8 days, with one network randomly selected each day. The table below shows the actual order determined by random draw:
ABC—July 6 (Wed)
FAM—July 7 (Thr)
FOX—July 9 (Sat)
MTV—July 10 (Sun)
ESPN—July 11 (Mon)
CBS—July 12 (Tue)
CNN—July 16 (Sat)
NBC—July 17 (Sun)
a. What is the probability that ESPN was selected on Monday, July 11?
b. Consider the four networks chosen for the weekends (Saturday and Sunday). How many ways could the researchers select four networks from the eight for the weekend analysis of commercials? (Assume that the assignment order for the four weekend days was immaterial to the analysis.)
c. Knowing that the networks were selected at random, what is the probability that ESPN was one of the four networks selected for the weekend analysis of commercials?
Workers’ unscheduled absence survey. Each year CCH, Inc., a firm that provides human resources and employment law information, conducts a survey on absenteeism in the workplace. The latest CCH Unscheduled Absence Surveyfound that of all unscheduled work absences, 34% are due to “personal illness,” 22% for “family issues,” 18% for “personal needs,” 13% for “entitlement mentality,” and 13% due to “stress.” Consider a randomly selected employee who has an unscheduled work absence.
a. List the sample points for this experiment.
b. Assign reasonable probabilities to the sample points.
c. What is the probability that the absence is due to something other than “personal illness”?
Consider the Venn diagram in the next column, where
Find each of the following probabilities:
g. Are events A and B mutually exclusive? Why?
Study of why EMS workers leave the job. An investigation into why emergency medical service (EMS) workers leave the profession was published in the Journal of Allied Health (Fall 2011). The researchers surveyed a sample of 244 former EMS workers, of which 127 were fully compensated while on the job, 45 were partially compensated, and 72 had no compensated volunteer positions. EMS workers who left because of retirement were 7 for fully compensated workers, 11 for partially compensated workers, and 10 for no compensated volunteers. One of the 244 former EMS workers is selected at random.
a. Find the probability that the former EMS worker was fully compensated while on the job.
b. Find the probability that the former EMS worker was fully compensated while on the job and left due to retirement.
c. Find the probability that the former EMS worker was not fully compensated while on the job.
d. Find the probability that the former EMS worker was either fully compensated while on the job or left due to retirement.
New car crash tests.Refer to the National Highway TrafficSafety Administration (NHTSA) crash tests of new car models, Exercise 2.153 (p. 143). Recall that the NHTSA has developed a “star” scoring system, with results ranging from one star (*) to five stars (*****). The more stars in the rating, the better the level of crash protection in a head-on collision. A summary of the driver-side star ratings for 98 cars is reproduced in the accompanying Minitab
Printout. Assume that one of the 98 cars is selected at random. State whether each of the following is true or false.
a.The probability that the car has a rating of two stars is 4.
b.The probability that the car has a rating of four or five stars is .7857.
c.The probability that the car has a rating of one star is 0.
d.The car has a better chance of having a two-star rating than of having a five-star rating.
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