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- The following diagram illustrates a16-team tournament bracket, in which the 16 participatingteams are arranged on the left under Round 1 and the winnersof each round are added as the tournament progresses. The top team in each game is considered the “home” team, so the topto-bottom order matters.To seed a tournament means to select which teams to play eachother in the first round according to their preliminary ranking.For instance, in professional tennis and NCAA basketball theseeding is set up in the following order based on the preliminaryrankings: 1 versus 16, 8 versus 9, 5 versus 12, 4 versus13, 6 versus 11, 3 versus 14, 7 versus 10, and 2 versus 15.48Exercises 37–40 are based on various types of eliminationtournaments. (Leave each answer as a formula.) In a randomly chosen seeding of an 8-team tournament,what is the probability that each team plays a team withadjacent ranking?High school seniors with strong academic records apply to the nation’s mostselective colleges in greater numbers each year. Because the number of slotsremains relatively stable, some colleges reject more early applicants. Suppose thatfor a recent admissions class, an Ivy League college received 2851 applications forearly admission. Of this group, it admitted 1033 students early, rejected 854outright, and deferred 964 to the regular admission pool for further consideration.In the past, this school has admitted 18% of the deferred early admission applicantsduring the regular admission process. Counting the students admitted early andthe students admitted during the regular admission process, the total class sizewas 2375. Let ?, ?, and ? represent the events that a student who applies for earlyadmission is admitted early, rejected outright, or deferred to the regularadmissions pool.a. Are events E and D mutually exclusive? Find (? ∩ ?)b. Suppose a student applies for early admission. What…The television show CSI: Shoboygan has been successful for many years. That show recently had a share of 19, which means, that among the TV sets in use, 19% were tuned to CSI: Shoboygan. An advertiser wants to verify that 19% share value by conducting its own survey, and a pilot survey begins with 12 households have TV sets in use at the time of a CSI: Shoboygan broadcast.
- How many ways are there to select 3 candidates from 8 equally qualified recent graduates foropenings in an accounting firm?According to scientists, the cockroach has had 300 million years to develop a resistance to destruction. In a study conducted by researchers, 6 comma 0006,000 roaches (the expected number in a roach-infested house) were released in the test kitchen. One week later, the kitchen was fumigated and 18 comma 10718,107 dead roaches were counted, a gain of 12 comma 10712,107 roaches for the 1-week period. Assume that none of the original roaches died during the 1-week period and that the standard deviation of x, the number of roaches produced per roach in a 1-week period, is 1.61.6. Use the number of roaches produced by the sample of 6 comma 0006,000 roaches to find a 9595% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house. Find a 95% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house.The television show Lett3rs has been successful for many years. That show recently had a share of 19, which means, that among the TV sets in use, 19% were tuned to Lett3rs. An advertiser wants to verify that 19% share value by conducting its own survey, and a pilot survey begins with 10 households have TV sets in use at the time of a Lett3rs broadcast. If at most one household is tuned to Lett3rs, does it appear that the 19% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Lett3rs unusual?) A. no, it is not wrongB. yes, it is wrong